Is AppleCare+ International?

I am not sure about the 'Theft' part, I have never heard of it. I got AppleCare+ for my iPhone 13 Pro Max in Canada. During a trip to the US, I left it on top of my car and drove off. I heard it fall off my car and stopped to get it. By the time I did it was already run over by another car and was badly damaged. Apple replaced it under AppleCare+ in LA right away. The only problem was the SIM was also broken :(

https://www.apple.com/legal/sales-support/applecare/applecar...

4.1 Hardware Services and ADH Services Apple may restrict Hardware Service and ADH Services to the country where the Covered Equipment was originally purchased.

And scrolling down...

Apple will not provide Hardware Services or ADH Services in the following circumstances: ... (c) To replace Covered Equipment that is lost or stolen;

The document actually contains remarkably little by what is covered under Theft & Stolen...

HOWEVER

https://support.apple.com/iphone/theft-loss-claims

This page explicitly mentions United Kingdom being covered when TRAVELING. Not sure how that works if you move there.

Not sure about theft, but I bought my iPad in Romania, moved to Australia and had it replaced in US when I was traveling there because it kept crashing and Apple Support folks in Apple Store detected some stability issues. All for zero cost