@Davud
You can report your phone as lost or stolen in Self-Serve. You don't need to know the IMEI to do this.
This immediately suspends service to the account, the number, the SIM card. So you won't have to pay while you're unable to use it. And you won't have to pay for somebody else trying to consume it. (I think this causes some problems with Rewards which would normally be allocated during the halted plan cycle, assuming Public Mobile still hasn't fixed these problems, but that's a minor inconvenience compared vs the chance of having your plan and add-on provisions depleted by a thief.)
Public Mobile will have a log of every phone/device (every unique IMEI) that your SIM card has been plugged into. But for some reason they're usually reluctant to share this information.
I'm not sure why your insurance claim would require an IMEI to be valid. But then again, I've endured countless other pointless stupid bureaucratic boxes over the years, a mighty insurance institution evolving into a typical technologically-backward corporate dinosaur is quite plausible. Still, if you lack an IMEI number (which, strictly speaking, your insurance company doesn't need and can't use for anything) then I suppose you can try just zeroing the field. It's always a fifteen digit string of numerals, often grouped (just for visual convenience) into three groups of five digits each, 00000 00000 00000.
In the future, you can lookup how to use your phone's (every phone's) built-in IMEI/MEID/ICCID display functions. And take a screenshot.
