I bought iphone with applecare but system weren't able to link my AppleCare plan to my Apple ID.

Apple Car is for a Device not for an Apple ID

You can use Apple ID with many devices.

Select your device serial number for linking not Apple ID.

Then contact Apple support as directed.

Where did you get the phone? What country are you in now?

AppleCare+ with theft and loss is only available in the US as far as I know. AppleCare+ can only be applied to a device sold in the same country.

Thank you for your advice. I have allready done that, spended 6 hours of free time on call. They said that i should change my region and it will work. But after this the problem is still same. I tried another call/chat/ email/ opening case. Nothing helped. So contacting the support as you say doesn’t help me either.

Same problem, same email. Can’t finish the link even after calling the support.

You're welcome. Although my response wasn't directed at you.

I don’t have theft/lost. I have sucefully purchased the A+ on my phone. It says Covered. But I am getting same error as on the screenshot above.

And you have provided no more information than the OP as to the circumstances...

Where did you buy the phone?

When did you buy the phone?

What country are you in now?

Where did you purchase the AppleCare+ coverage?

Sorry but your questions are pointless, because I have my iPhone covered with AC program.

1) Where? On the internet.

2) When? 57days before now

3) Now? I am in Czech Republic, but I am working in the US

4) Where? On the internet. You can purchase AC+ program to any iPhone before 60days from activating. As the coverage info says