How can a woman terminate an Islamic marriage that is not officially recognized in Germany, especially if the husband refuses to grant a divorce?

The marriage contract is valid if its pillars are met, even if it is not officially documented, but it should be documented. A woman is not permitted to seek divorce unless there is a necessity, based on the saying of the Messenger of Allah (peace be upon him): "Any woman who asks her husband for divorce without any strong reason, the scent of Paradise will be forbidden to her." If her dislike of staying with her husband is due to his bad character or shortcomings, then she is allowed to seek divorce and take all her rights. However, if the dislike is from her side without any fault in him, then she must seek khul' (divorce at the wife's instance) by returning what the husband gave her as mahr (dowry). It is advisable to resort to people of goodness and wisdom to reconcile between them, and if that is not possible, the problem must be resolved according to the rulings of Islamic Sharia.