If you can rule out pain first, along with any respect issues on the ground, there's a fee things I have tried and would suggest trying. If you aren't experienced at all with rearing, I would first and foremost suggest telling your friend to send it to a trainer experienced with it.
One of the first things I will do with a rearer (last horse I was leasing/training) is get a bend in them. Horses are rather self-preserving animals if they aren't purely in fear/pain, so they're not likely to go up when they know they aren't balanced enough to come back down at their will and most likely won't land on their feet again, a bend does this to them. They can be any size circle (I suggest circle because it gives the horse the least chance to refuse movement, along with the quickest option)as long as the horse keeps moving, a stopped horse can rear, a cantering horse cannot. Or you keep the horses head flexed to one side until they stop moving and then quickly cue them forward just as they stop. I usually love the idea of making them work like they're going to die for what they did.
A crop/whip/egg/water balloon is also a great way, and it does work from what over heard, but you need to know how and be able to do so correctly. Knowing isn't the hard part, actually doing so at the correct time is. If you're just moseying along and your horse freaks and rears, are you goingto have the reaction time to even think of hitting the horse between it's ears -as it goes up-? A lot of the time I don't, so I don't use this method too much. I'd much rather not correct my horse for something wrong, than just hit it for nothing and confuse it. I don't recommend using this method for this reason, although if experienced and able it is a great method.
It also depends on how big of the rear, I did slightly different things for different sized rears. For big rears, I can usually think fast enough to grab my reins and yank their head to one side before they're already up, and I prefer this method if the "work their ass off" method doesn't work well. In my experience, it makes the horse think that they're now falling because of their stupid above-ground stunt they just pulled; horses are smart, they don't like to risk injury to themselves if they can avoid it. Little hops off the ground are no big deal to me, and I can deal with them as if they weren't there in the first place and not care, but I can see where this is unsafe for an inexperienced child. So, in that case, I would just handle it the same as I would the bigger rears, since you really don't want this.
In response to the previous post, I would also refrain from flipping a horse over. I've heard stories of horses that ended up with broken withers from being flipped without a saddle on, and I'd be scared for both my horse and my $1500+ saddle. Albeit, I do ride western and you didn't state which you rode; but if a horse can break it's withers (a TB I believe it was) without a saddle, imagine what it could do with a heavy duty western saddle. I don't see that image as too attractive.
I would also have to say that most horses (about 97.8% my guess) will always revert to rearing when in intense situations that cause it undue stress, pain, fear, etc. I will never trust Dude to not rear with arena work, because he use to be able to get out of it because of his leaser last show season. He knows sure as all get out that he doesn't rear with me anymore (other than the occasional freak out because he's leading on a trail and he thinks he sees something I don't, like a horse eating tree or a deer), but I would never put a complete novice on him and let him/her try to take him to do a barrel pattern.
If you treat a horse like it -will- rear, it will most likely rear, if you're scared of it rearing, it may very well rear to get you off because it doesn't trust fear, etc. I would say that it would just be bette to sell/trade the horse and get a newer broke one for the girl, but I can understand wherethat is not the most practical choice, although it would be the safest, imho. But the owner/mother has to decide that for herself what risk she should allow her daughter to take on a horse and what is too much. I agree that rearing is one ofthe most dangerous things a horse can do, and I wouldn't take that lightly if it was my child.
But, good luck, and I hope I helped a little.
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