If she’s in need of a self esteem boost, then she may see him wanting to move in of confirmation that he really loves her.
I think you need to impress on her that, especially as we get older, moving in together is not a natural next step and show of love and commitment.
Unfortunately, when your self esteem is down, being told that you’re being bloody stupid in this decision is counter production. Being told you’re making bad decisions doesn’t build the confidence you need to make good decisions.
I would point out gently, but not labour, the point about convenient timing.
I would be perhaps neutral rather than negative about him moving in, and then focus on the practicalities - “will be able to pay his share though?” / won’t it annoy you to be paying for him?”
Of course - you know your friend... if it’s going to work to tell she needs her bloody head reading, then go for it!
Because you’re right... these red flags are as big as they come. Very obvious.
And you know what? Even if he was the loveliest guy with no red flags, whose parents wanted him to stay forever - she still should move him in and subsidise him.