Hi @beebson
You can apply for redistribution at any time in the asylum process. However, for up to 18 months you are obliged to stay in the initial reception cetnre (Erstaufnahmeeinrichtung). Then you are assigned (Zuweisung) to a particular place in Germany. If you are still in the initial reception centre, then you have to inform the authorities about your Ausbildung in the hope that they will take this into account when deciding where you are to go. You only have a clear right to move to a specific place if there are core famly members living there. All other reasons come under the category of 'humanitarian cases' (e.g. medical or educational reasons) and it is at the discretion of the authorities whether to take them into account. If refused, you can file an appeal with the court.
If you have already been moved to a specific area, then you can apply with the authorities to move also. This is called Umverteilung. It depends whether you wish to move within a state of German or to another German state (Bundesland) to know which authority is responsible. Again here there is only a clear right for family reasons; other humanitarian cases like having an Ausbiludng can be taken into account. The state of Lower Saxony (Niedersachsen) for example, has issued instructions that in that state asylum seekers are allowed to move for an Ausbildung. There may be similar instructions in other states.
Here you can read in detail via online translation about the distribution process:
https://***-nds--fluerat-org.translate.goog/leitfaden/4-status-aufenthaltsgestattung/wohnen-umziehen-residenzpflicht/?_x_tr_sl=de&_x_tr_tl=en&_x_tr_hl=en&_x_tr_pto=wapp
Best,
Éanna