My mom’s iPhone got stolen while she was out shopping, Find My iPhone is enabled but we’re stuck because:
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She doesn’t remember her Apple ID
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The linked gmail address has 2FA
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Email does not have an alternative backup option enabled
What’s the best bet to try and find it?
Unfortunately with those barriers you won’t be able to find it. Hopefully you can get a replacement phone soon and to prevent this in the future make sure she remembers her Apple ID info or have it written down somewhere safe at home to hopefully track the phone but even then a stolen phone is likely gone for good.
To reduce the chances of her new phone from getting stolen in the future make sure she keeps it secured in a bag or purse and well attached to her person. Some criminals are so brazen they will even snatch phone out of a persons hand depending on the area.
The snatch has happened to me once. And from then my phone on pocked always locked with custom password.