One traveling abroad with a vehicle not registered in his/her name needs a user permit “Benützungsbewilligung/Vollmacht in german”. You you get it from the German Automobile Club like avd which is sufficient to travel abroad with someone’s vehicle.
But for Ukriane it should be notarially attested (see the source – Vollmacht, Federal Foreign Office of Germany, Ministry of Foreign Affairs Austria and Honorary Consul Ukarine).
For fruther information you should call avd, adac or other Automobilclubs in Germany.
Source: ÖAMTC in Austria
Source: AVD in Germany
Source: Vollmacht for Ukraine – notarized
Source: Federal Foreign Office Germany – “Einreise mit Kfz”
Source: Ministry of Foreign Affairs Austria – “Verkehr & Klima”
Source: Honorary Consul Ukarine- “Ratgeber für Reisende”
Edit: One can`t say that information posted on differnt forums (without sources) is valid and the information posted on Federal Foreign Office of Germany or Austria which even recommend different Autommobileclubs for further information on Ukraine is invalid.
Credit:stackoverflow.com‘