AT&T replace iPhone still be AppleCare?

When I bought my iPhone, I got AppleCare+ and the AT&T insurance. I was randomly thinking, if my iPhone was replaced by AT&T, would I still be AppleCare+ on the replaced iPhone?

AppleCare+ covers the serial number and IMEI number of the device/Phone that you register with Applecare.
This keep people from turning in an older phone that is out of warranty, for one that is still under warranty to get replaced or repaired, so once the serial/IMEI changed, you could not use AC+ on any other phone, unless you can transfer the coverage to the replacement phone, and for that you need to call and ask AC. And that replacement would HAVE to be through AppleCare, NOT AT&T.

Transfer your AppleCare plan

If you sell or give away your Apple device, you can also transfer the ownership of your AppleCare Protection Plan or AppleCare+ in regions that allow it. You can also transfer your AppleCare coverage plan between your own devices that are the same type of product and within 30 days of your original device purchase.

When we replace your device instead of repairing it, we'll automatically transfer your plan to your new device. If transfer of coverage isn't possible, we'll offer other options.

It should be.