Wait, that's what she has to do. Her boyfriend still has some maturing to do.

Well, if his mom comes to accept them, it would be easier for them in the future. Still, I don't think now is the time for them to get married. She must wait some more.

girls want to move along with men, its ok to ask for marriage.bt the guy must want it too. what if he gets biased by the parent's decision and decided to turn away...

That's the risk of asking the guy to marry her. If she decides to do it, she must accept that this is a possibility.

I still believe that guys should be the one to ask. The girl should wait or just drop hints at the most.

Well if that guy seems controlled by his mum then all your friend has to do is to convince her future mother-in-law that she's the perfect wife for her beloved son..pretty obvious/!!! he's going to ahve to heed to mom's wishes!!
now it all depends if mother-in-law really likes her..try to buy her some gifts to mellow her..