If you view DWP as being suspicious of everyone's motives, it doesn't really matter when he moves in does it?
If it's during the review, according to you they'll assume you're playing catch-up by telling them about something that has been ongoing - him actually living with/staying over most nights etc.
If you wait until after the review then, according to your logic, they'll assume you've had a fright during the review process and are covering your arse going forward.
Regarding losing money, I'd imagine the benefits amount your family receives will reduce once they factor his salary into household income. They will see your children being supported by 1.5 salaries, rather than the 0.5 salaries at present.
Personally, I think there are probably other issues to consider too:
a) how long has he been a 'changed' person?,
b) how much is his motivation to move in tied in to him getting away from his mother?,
c) are you confident him moving in is in the best interests of your children?,
d) will you have the financial resources to provide for your children should there be issues/delays with your joint application for UC?