hello ,
As from my experience it’s really hard to move one city to another city in Germany . I did the Same process with my 6 month Aufenthalsttung on 2016. Only got accepted by 2018 April. You can see the time difference. It’s because of The strong requirements. You must have a job with permanent contract on new city , also you have to find a house on your own , and submit the rent contract ( Miet bescheinigung ) . Also you need to attach the letter with the reason of your request. It must be a worthy reason. Examples like new job, or family reunions something
If you submit those documents only you can get the process begins, otherwise they won’t accept your request . Even if you bring all those documents, it’s takes minimum 6 months time to process . So be prepare of all those documents and all the best