A possible schedule and route is mentioned on Wikitravel’s South Iceland page when talking about the Skógafoss waterfall:
Skógafoss is 60 m tall and 25 m wide and comes from the river of
Skógá. The falls have been protected since 1987. Access to the falls
is open all year round and there is no admission. A trail leads to the
top of the falls (via metal stairs to the right of the waterfall) and
up the Skógá river valley. This trail eventually ascends all the way
to the Fimmvörðuháls pass between the Eyjafjallajökull and
Mýrdalsjökull glaciers before descending to Þórsmörk; the complete
hike from Skógar to Þórsmörk generally takes two days. Day hikers can
follow this trail as far as they like along the Skógá river, they will
be rewarded with views of more than a dozen waterfalls.
So it looks like you can start in Skógá, do a two day hike, and end up in Þórsmörk.
Credit:stackoverflow.com‘
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