Can I purchase AppleCare theft and loss for a stolen iPhone within 60 days of purchase?

No.

You can't purchase insurance to cover your house burning down AFTER your house burns down.

You can't purchase insurance to cover your car being stolen AFTER your car is stolen.

And you can't purchase insurance to cover your iPhone being stolen AFTER your iPhone is stolen.

In any of those cases, if you did purchase insurance, the insurance would be held to be null and void. If you were to purchase insurance and then try to collect on it, you would likely be prosecuted for insurance fraud.

No you can't. And that would be fraud if the phone was stolen. I can't believe you'd even ask such a question. What you can should do, is contact the credit card company you used to make the purchase to see if they have any theft protection options. But trying to buy AppleCare+ after the phone was stolen is just plain and simply wrong and unethical.

Other Rob S. wrote:

Hey, what I figured. I was going to be upfront about it. Or I wouldn't have asked.

I'm glad you were upfront about it. Still surprised you'd ask such a question. I'm sorry your phone was stolen. I hope your credit card company has some theft protection.

The volume of the ensuring fraud would bankrupt nations.