When asylum seekers or people with Duldung want to move within Germany, they must submit a „redistribution application“. All recipients of asylum seeker benefits are generally obliged to live in places they have been assigned at the beginning. This is called a "residence requirement". Moving to another location (redistribution) is rarely allowed. To apply, you must submit a "redistribution application" to the Immigration Office responsible for you. You are only entitled to the redistribution if your spouse or underage child lives in another location. Otherwise, the authorities can decide whether or not to approve the relocation application.
To have a chance of success you need solid reasons such as caring for sick family members, the availability of a specialised and urgently needed doctor, etc. You can take legal action against the rejection of an application for reallocation before the Administrative Court. However, the chances of success for such lawsuits are quite slim. Since 2016, the federal states have also been able to stipulate a place of residence for recognised refugees or asylum seekers for up to 3 years. Refugees who take up vocational training, study or a job subject to social security contributions of at least 15 hours per week and earn enough are exempt from this rule.