Did German soldiers receive pay after the Allied invasion?

It is my understanding that while the regular Wehrmacht soldiers were generally entitled to pay and pensions, members of the SS and Waffen-SS were not. The SS was declared a criminal organisation during the Nuremberg trials and so all payments and service was stopped at that point. Conscripts, after 1943, were exempt from the declaration of criminal activity.

Stein, George (2002) [1966]. The Waffen-SS: Hitler's Elite Guard at War 1939–1945. Cerberus Publishing. ISBN 978-1841451008.

ACTUALLY, The last German soldiers in WWII were paid up until 1948. These were the naval mine clearance men, who were NOT discharged at the end of the war, but had their service extended involuntarily until 1948.

Other troops were discharged and sent home, but these men were told they were NOT going to be discharged, and were to continue serving until the mines were cleared, which they largely did. They continued wearing WWII German uniforms until they got their own special uniforms after the war.

The man who designed the Biber submarine was one of those killed during the demining operations. They had a LOT of deaths and a LOT of accidents. So some naval men served from 1939 to 1948. These would be the longest serving German soldiers in WWII.

Yes, the German soldiers were being paid after June 6, 1944.

Consider the case of the Merkers mine, where most of the gold reserves of Germany, plus a lot of looted artwork and precious metals, plus a substantial amount of printed Reichsmark and the plates to print them, had been moved not long before the Reichsbank in Berlin (the normal repository for Germany's financial reserves) had been destroyed by bombing. Third Army overran this area and were told about the contents of the mine by French and Polish workers who had moved the contents into the mine. This prompted considerable interest from high command.

Eisenhower and Patton were touring the mine, guided by Col Bernard Bernstein, deputy chief of the financial division of SHAEF, who had been detailed to supervise the safeguarding and inventorying of the mine.

Bernstein also showed the generals the art treasures, plates the Reichsbank used for the printing of the Reichsmark currency, and the currency itself. While they were looking at the latter, a German official said that they were the last reserves in Germany and were badly needed to pay the German army.

So, yes, the soldiers were being paid in Reichsmark right up until the monetary reserves of Germany were captured.

The German state always cared for its soldiers and veterans. The soldiers were paid for as long as possible (long after June 44), receiving regular soldier's pay ("Wehrsold"). After the war they, and/or their relatives, received pensions and other benefits as soon as possible, as long as possible and as widely as possible, even exploiting loopholes in legal definitions; running contrary to publicly emphasised politics.

Let's start with the "deeper question":¹

As for the regular pensions of regular Wehrmacht soldiers, the Allies – now after the war having the last word on everything regarding Germany until 1955 – had differing opinions on and arguments about that:

Colonel Gomme-Duncan: Does not the hon. Gentleman agree that these officers and men earned their pensions as soldiers before the war, and surely in every sense of justice are entitled to them? We should not expect the Germans to take away the pensions of our men. (15 March 1948 → Commons Sitting → Germany)

But the general agreement was reached that soldiers were entitled to pensions.

The actual pay during the war for active personnel was never in question at the time, from neither side.

After D-Day soldier's pay continued orderly and well into the last weeks of 1945. Although, as much as the organisational structure of Reich and Wehrmacht crumbled near the end, pay in terms of money became increasingly less useful.

Even though money was loosing utility near the end of the war and shortly after the capitulation, the Wehrsold was paid out with meticulous reliability. "As long as possible" mentioned in the introduction to this answer means, that as long as soldiers were attached to their organisational structure, Wehrsold was paid. This might be read as "right until the end in May 1945". In reality Wehrsold was paid even after that point:

Showing that some individuals were paid for up until October 1945. This is no fluke. Although not the norm this applies to quite a number of soldiers. For this particular individual it was:

It finally surrendered to US troops near Vienna, Austria on May 5, 1945. It is possible that Woditsch was part of this division, if he joined them after recovering from his illness or injuries in time, and, if he survived the war, ended up as a POW of the Americans. Interestingly, he was still paid a salary of 36 Reichsmark in October 1945, indicating that he survived the war.

(Picture from: An Ss Soldbuch & Id Tag To The Ss Volunteer Cavalry Regiment 1 & POW)

You might wonder how a soldier got his regular pay even after May 1945. The organisational structure of the Wehrmacht was not immediately and completely dismantled everywhere! After the unconditional surrender in the second week of May 1945 the German head of state Karl Dönitz continued a German government in Flensburg, very weakened and de facto without any much territory to control, trying to negotiate with the allies over some details. This ended only on May 23rd when all remaining troops surrendered and together with the officers were captured as prisoners of war.

The mystery of continued payments even after May 23rd, 1945 is explained in how British and Americans organised the adminstration of their "Disarmed Enemy Forces" (DEF) or "Surrendered Enemy Personnel" (SEP). After the Fall of Berlin English and American forces corralled German soldiers, but left them with a certain degree of self-administration. In the American sector:

Ende Mai […]. Die Militärkommission der 6. USArmy Group […]. Die enge Zusammenarbeit blieb also gewährleistet. Das war um so nötiger, als sich das Schwergewicht nun zunehmend auf die Geldversorgung verlagerte. […] Die Militärkommission überließ daher Verfahren und Verantwortung für die ordnungsgemäße Durchführung dem Oberbefehlshaber Süd […] Sie stellte als Grundbetrag 200 Millionen Reichsmark (RM) in Aussicht, von denen die Hälfte auf einem Girokonto der Deutschen Reichsbank – so hieß sie damals ja noch – in München für unbaren Geldverkehr und als Reserve verbleiben sollte, während die anderen 100 Millionen RM der Leitende Intendant für die notwendigen Zahlungen zu eigener Verfügung erhielt. Damit konnte zunächst der Wehrsold, auf den ja auch für die den Kriegsgefangenen rechtlich gleichstehenden Entwaffneten ein Anspruch bestand und dessen Zahlung, je nach der Kassenlage der Einheiten, seit dem 10. Mai eingestellt worden war, wieder gezahlt werden.
(Summary: after the payments had stopped after May, 10 in 1945, the Americans ordered money transfers and authorised local authorities to distribute the money to the soldiers who still had a legal claim on the money.)
(From: Kurt Nothnagel: "Die »Dienststelle Fritsch« Ein Beitrag zur Geschichte der Versorgung der entwaffneten deutschen Wehrmachtangehörigen in der amerikanischen Besatzungszone, 1945-1947", Militärgeschichtliche Zeitschrift, Volume 21, Issue 1, 1977.)

The last remnants of the Wehrmacht were only dissolved in December 1945 and the Wehrsold stopped.

Returning to the pensions, still paid out: The currently official stance on pension claims and benefits is:

Die Zeit als Kriegsteilnehmer bei der deutschen Wehrmacht wird nach der Vollendung des 14. Lebensjahres als Ersatzzeit anerkannt.
(The time as a war participant in the German Wehrmacht is recognized after the completion of the 14th year of life as a time eligible to count for a pensions claim; the time in the army counts as compensatory for regular work time with associated contributions to the pensions fund.)
Info from an answer to a request to the official pensions institutions in Germany)

After 1956, every deed anyone did by order of the German Reich in officially recognised organisations or institutions was bureaucratically classified as regular work, eligible for pensions, even without the claimants having paid into the funds of solidarity otherwise required for that.

For more details on how and when pensions to soldiers were agreed upon and came to be paid after the war, cf.
Alaric Searle: "Wehrmacht Generals, West German Society, and the Debate on Rearmament, 1949-1959", Praeger Frederick: Westport, 2003.
The above is exclusively for West-Germany and unified Germany after 1990. The GDR handled things a little differently, and less generous. For these details:
Johannes Frerich & Martin Frey: "Sozialpolitik in der Deutschen Demokratischen Republik", De Gruyter: Berlin, Boston, ²2014. (Some extracts on GBooks, p24f.)

_{1: This version of the answer was self-censored by the original author of this post due to popular request. A more detailed explanation is found in version 15 in the edit history. Do not go there and read that version if you are easily offended.}