Assalamu alaykum Ustadh. I made hijrah to Egypt but am still registered as a resident in Germany. Is it Islamically permissible to continue receiving German unemployment benefits based on my years of employment there?

If their own conditions still entitle you to it while you are living outside the country, taking it is not a problem. If the entitlement depends on residence and you are holding a registration that does not match where you actually live, then it is money taken without right and a breach of the covenant your residence rests on, and what was taken that way is returned.