The other husband spouse claims another son as dependent. But, that son's most of expenses paid by the mother filing as head of household, even though not claiming him under her return. Can this son's expenses be considered by mother as qualifying expense for deduction? The expenses are cpvered under Flexible Spending account.

You CAN claim the child's daycare expenses as the Head of Household as long as the parent who is claiming the personal exemption is not also claiming those expenses.