O_O I apologize if this sounds rude, but that horse does not need to be jumping much over 2'6" for a while. In the first video, he is so incredibly strung out, and in the second video he's not much better.
Quality of canter = quality of jump. If you have a crappy, long, unbalanced canter your horse isn't going to jump in a scopey, nice form. Period. End of story. This horse needs to go back to ground work to become more adjustable, responsive, and balanced. And he needs to cut out that head tossing thing. It's one of the most irritating things I see in a good deal of horses that jump nowadays.
Now, to answer your question, for the most part I've always been told you can fix a horse with a bad front end but you really can't fix a horse that doesn't have a catty, snappy hind end. So with this guy I would say yes, you can improve his front-end style. It's going to take a lot of want I mentioned above though. He needs to be able to maintain an established, balanced canter and be responsive to you, the rider, without throwing his head around. I''d be doing a whole lot of flatwork with him and once he starts to become more established in his flatwork I'd be doing a lot of grid-work with him. He needs to learn to jump from the base of the jump, not from a stride and a half out, and he won't be physically strong enough to jump from the base of the jump until he can be balanced and relaxed in the canter.
I know you said he's green and I can definitely tell. If you friend wants a fun, reliable horse, this is not the horse for her right now and she should keep looking.
"Always be yourself. Unless you can be a unicorn. Then, always be a unicorn."