Dear @Vladimir88,
Thank you for reaching out to the Wefugees Community!
In general, it is possible to change the company/employer during the "Ausbildung". However, if you don't want to lose time or repeat a year at school, you should carefully prepare and plan your change. First of all, you will need to apply again and search employers, offering the same type of Ausbildung.
I made some research and found this website, which nicely describes the necessary steps.
In case you are holding an "Ausbildungsduldung": Once you quit your Ausbildung, you have six months to find a new one/sign a new contract. Otherwise your document will expire.
I hope this helps and please feel free to get back to us with any further questions.
All the best,
Meike