Actually the cheapest way is to have a good repair shop do it. However ... the screen is going to run around $150, and the phone is worth about $300 if it's in good condition aside from the screen, so add a profit for the shop and labor and you won't be making any money.
We've seen many people here who have bought a screen and replaced it themselves - then came here asking for help because the phone stopped working. By the time you get finished replacing everything you break (and you will the first few times you work on a cellphone, which is why repair shops keep unrepairable phones around - for new techs to practice on), you'll have spent more than the retail price of the phone.
Do her a favor - find a shop that will trade you the phone for temporarily connecting a working screen to it so you can get her data off. That way, at least you won't lose any money.
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