The payment would be deductible by you only if it qualifies as alimony; but you did not give enough facts to determine whether the payment qualifies as alimony. It probably does qualify as alimony, unless you were considered members of the same household at the time the payment was made. The Q & A, below is from an IRS document, and I believe it gives the rules you have to know to make the determination. However, if it does qualify as alimony, she would definitely have to show it as income.
Q-9: What are the consequences if, at the time a payment is made, the payor and payee spouses are members of the same household?
A-9: Generally, a payment made at the time when the payor and payee spouses are members of the same household cannot qualify as an alimony or separate maintenance payment if the spouses are legally separated under a decree of divorce or of separate maintenance. For purposes of the preceding sentence, a dwelling unit formerly shared by both spouses shall not be considered two separate households even if the spouses physically separate themselves within the dwelling unit. The spouses will not be treated as members of the same household if one spouse is preparing to depart from the household of the other spouse, and does depart not more than one month after the date the payment is made. If the spouses are not legally separated under a decree of divorce or separate maintenance, a payment under a written separation agreement or a decree described in section 71(b)(2)(C) may qualify as an alimony or separate maintenance payment notwithstanding that the payor and payee are members of the same household at the time the payment is made.
