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Does it have an APNS token? Is it possible to send yourself a push notification and see what app it appears to come from?

You need an appropriate cert for that.

...assuming this has any connection to LEA

It would be interesting if you and others with their device on the list could come up with a list of apps that you've had installed.

How does that prove that an FBI laptop was the source of this information (per the grandparent post's question)?

Your grandparent asked two questions. He answered the other one.