Hi @Anastasia I,
Unfortunately, I only have information about the reverse situation, i.e. if someone has temporary protection in Poland and then comes and applies for it here in Germany. The German authorities have made clear that this is possible.
I recommend you contact organisations working in this area in Poland or Lithuania
This organisation provides free legal aid in Poland:
https://***.pomocprawna.org/en/special-law-for-people-fleeing-ukraine---a-short-guide
For Lithuania you could contact this organisation:
https://***.refugeeslt.***/
I advise you to clarify this before leaving Germany and trying to register there. Once you apply for temporary protection in another EU country, your residence permit here becomes invalid.
With your residence permit, you are entitled to travel throughout other countries of the Schengen Zone for 90 days. Germany is your place of residence and does not count as travel in the Schengen Zone. Here it is also answered on a governmental website:
https://***.germany4ukraine.de/hilfeportal-en/entry-residence-and-return/entry
Best,
Éanna