Is it permissible to postpone the legal marriage contract and suffice with the Islamic marriage contract to preserve the state grant allocated to daughters of Mujahideen, which ceases upon marriage, due to the girl's need for this grant given her husband's difficult financial circumstances?

If the grant is conditioned on the woman not marrying, then this condition must be observed. It is not permissible to take the grant if you marry, and the fact that your husband is in financial difficulty does not make it permissible to take it, because you accepted to marry him despite knowing of his poverty.