Technically, he would not qualify for the deductions (see the rules below); however, if he is sure the mother did not claim the third child, then if he does, the IRS may never question it. If they do, he will probably lose the deduction.
Unless the divorce decree specifies otherwise, the noncustodial parent is treated as providing more than half of the child's support and is therefore entitled to the exemption if:
1) The custodial parent signs a written declaration that he or she will not claim the exemption for the child, and the noncustodial parent attaches this written declaration to his or her return,
2) A decree or agreement went into effect after 1984 and states the noncustodial parent can claim the child as a dependent without regard to any condition, such as payment of support, or
3) A decree or agreement executed before 1985 provides that the noncustodial parent is entitled to the exemption, and he or she provides at least $600 for the child's support during the year, unless the pre-1985 decree or agreement is modified after 1984 to specify that this provision will not apply.
Noncustodial parent. The noncustodial parent is the parent who has custody of the child for the shorter part of the year or who does not have custody at all.