It is a little bit complicated: Some of you would like to just go on and work remotely in your regular Ukrainian jobs – as far as possible. But it is really important to register within the first 90 days of your stay in Germany.
When issuing the temporary residence permit, the foreigners authority will note on the residence permit that paid employment is permitted.
The foreigners authorities will also issue provisional residence documents already upon application. Such a provisional residence document already allows for self-employment or salaried employment in Germany. There is a lot more information by the Ministry of Interior.
After having received a permit, you can go on to work for your former employer. Make sure though to check with your HR colleagues whether e.g. there are legal questions you need to fix. Also, your Ukrainian health insurance might still cover your temporary stay abroad.
If you need a job, there are two new and specialized platforms offering thousands of jobs in Germany and other EU countries: