Is the marriage contract considered valid despite the non-registration of one of the agreed-upon conditions (the deferred dower - مؤخر) at the time of the marriage contract, and what are the consequences of that after eight months of marriage and the existence of marital problems?

The agreed-upon Mahr (dowry) between the husband and the wife or her guardian is what is considered valid. If a portion of it was deferred and the husband agreed to it, then it is a right of the wife. If the husband denies it, then it is incumbent upon the wife to prove her claim. It is advised to refer to the Sharia courts for a resolution in this matter.