As long as you have written permission, but check with INZ exactly what format etc the letter should take and what details they want included. I had the same situation - one child from a previous relationship. The letter I drew up and which his father signed was accepted by INZ, but we were never married. PM me your email and I'll scan it to you. My son turned 16 during the process, so that could have simplified things for INZ, so also check with almost_heaven what they required from her.