Thank you for your question
My name is Clare
I shall do my best to help you but I need some further information first
How many nights do they spend apart in the average week?
That is not "residing" with!
If they spent every night together just at the two different houses that oculd count - but not two or three nights a week in one or other of the properties!
Please ask if you need further details
If they spend more nights a week together than apart - of if he ceases to have his own home, then that is likely to be seen as cohabiting
A letter from her will be fine