No, you both can't put 7 months. So, in this scenario, if you are the custodial parent, then you would put 7 months and the program will ask about whether you have an agreement for the dependency. You would answer Yes that you have an agreement and Yes the other parent will claim the dependent. This will give you the EIC/CDC/HOH (cant be split) but not the dependency or CTC.
Then, your ex-wife would enter 6 months, and when she gets the questions about the agreement she would answer Yes that you guys have an agreement and NO, the other parent will NOT claim. This will give her the dependency and CTC.
But, to be clear, you have to be the actual custodial parent to claim the EIC etc, you can't just agree to allow one parent to put 7 months. Only the dependent and CTC can be agreed to be shifted. And, yes, one parent will have to paper file (like I said before, you can try to e-file first, but be prepared for a rejection and to have to paper file)
