is it a problem to buy an iPhone in a different country? My parents are traveling in Central America, and my mom's iPhone was stolen. She was going to buy another one in Honduras. After their trip wraps up in a month or two, she's going to come back to the US and the vast majority of her future usage will be in the US. 

I'm just wondering if there are any potential problems with this plan. I know that when you setup an iPhone you can choose a particular language, so that isn't a problem. 

One potential problem is it will probably cost her more, because she'll be buying without the subsidy she'd get from a US carrier. She knows about this and is willing to do it anyway, because she really likes sending photos to us from her trip. 

Are there any other technical or logistical issues? The big one I can think of is maybe the model she'll get will be setup for different cellular bands than the model she'd get in a US. But my information might be dated, perhaps this used to be a bigger problem last decade than now. Plus this is Central America, not Europe or Asia.

Anyway, this is a pretty wide-ranging question but thanks for any advice you can provide.

ALSO: Since this is a stolen iPhone situation, is there any Apple-specific thing you might recommend? We are already going to 1) Tell Verizon to switch her service to her new iPhone, and 2) Attempt to wipe the phone remotely using Find My iPhone. But I forget if it helps to tell Apple about the theft. This is an older model iPhone (5?) and not on the latest iOS so it might not have some of the latest anti-theft capabilities that I think they put in iOS recently (but forget what they were)
There are two issues:

First, while Apple's warranty is international, Apple sometimes limits overseas service to the country where the device was purchased, or requires users to return the item to the US for service. This stackexchange answer has more information.

Second, she must be careful to purchase a model which will cover the phone bands she expects to use. iPhones sold in different countries sometimes have different coverage, and often multiple models (band coverage-wise, not "7" or "8" or "X" - wise) are offered. This Apple webpage, for example, lists the models that will provide LTE coverage as well as the bands covered. (I know it's bad form to refer to an external page, but the info is far too large to copy-and-paste into this answer.)