How do I know if Italian SIM card will work in my phone?

You must google the frequencies of Motorola Moto G Pure xt2163-4 . Then google the frequencies used by the 4 main Italian companies: Tim, Vodafone, Wind3 and Iliad.

Any SIM card should work in an unlocked cell phone. All she needs to do is switch the current SIM card with the Italian one. You just need to decide if you want to order the SIM card and send it here, or have her pick one up when she's there. The first option is more expensive and she won't be able to use it till she's in Italy, but it will be more convenient. The second option will definitely save some money but she will have to find a SIM card retailer.

You might find some information at this site: https://thesavvybackpacker.com/buying-sim-card-data-italy/

As Dario suggests, what you care about is whether the phone you just bought supports the frequencies the Italian cell network uses. The SIM will work in an unlocked phone, but that's not the concern.

According to https://www.kimovil.com/en/frequency-checker/IT/motorola-moto-g-pure this phone supports some of the 4G bands so it should work but if you haven't opened it perhaps she can just buy a phone when she arrives in Italy The study-abroad program should have been giving students info on how to get set up with a phone.

Thanks for all the information. I have not opened it yet and still have 13 days to return. The information the school gave was very vague "any newer smartphone" so trying to get back in touch with them. School is already going to have SIM cards for them when they get there so I will find out which one. She will have her US phone with international plan if needed to use over WIFI . School just said that they require one with Italian SIM.