You can both file a tax return, but only one of you can claim his exemption. If he is your Qualifying Child, he would be your dependent and you would claim his exemption. He would be considered a student since he attended school for at least part of at least 5 months. If he moved out in July, he was living with you for at least half the year. If he is not filing a joint return, the main issue would be if he provided more than half his own support.
Qualifying
Child
1. The child must be your son, daughter,
stepchild, foster child, brother, sister, half-brother, half-sister,
stepbrother, stepsister, or a descendant of any of them.
2. The child must be (a) under age 19 at
the end of the year and younger than you (or your spouse if filing jointly),
(b) under age 24 at the end of the year, a student, and younger than you (or
your spouse if filing jointly), or (c) any age if permanently and totally
disabled.
3. The
child must have lived with you for more than half of the year.
4. The child must not have provided more than
half of his or her own support for the year.
5. The child must not be filing a joint
return for the year (unless that joint return is filed only to claim a refund
of withheld income tax or estimated tax paid).
