You convince him to give the kittens And mother, or at least the kittens up to you right now! Or call the humane society.
I had a couple kits last year that were very near death I honestly didnt' think they would make it, specially not with out there mother, but they did! It can happen, you just HAVE to get them out of there dear.
If you call the humane society, you do not have to give them your name, but if you do you can ask them to keep you as annonymous to this guy who has the cats. Not that they would mention your name anyways. Tell them the deal, and that you are concerned for the animals, that you have been to this place and SEEN these animals and that you fear they might die, HOPEFULLY the humane society will do something, I can't garuntee they will tonight or tomorrow, but as soon as they can IF you have a decent HS near you.
At very least if he gives them to you, then YOU can turn around and bring them to some rescue that does have space for them.
Even if you can take these cats and have them in your warm and feeding arms for a day or two it can make or break their life hun.
Do you think your friend would at least give you the kittens? Or at least offer "I'll take them off your hands for a little while, so you don't have to worry about it?"
I feel so upset now, not at you, but people like him.
Just reminds me so much of Avil and Meliah, they were really on their last leg, took me forever to get them from a dog rescue who had come across them, by the time I got them they were barely moving, but with in 2 days they perked up a little! And they have a happy home together now as young adults.