I'm trying to add a contact on Telegram, the specified number can be added through other phones, but not the same here:
[Name] is not on Telegram yet, would you like to invite them to join?
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You're trying to add a Telegram contact, which only work if this user has a Telegram account.
It's not just like adding a contact to your phone.
You can add this number to your regular contact list, and search it (by the saved name) in Telegram. If the user has a Telegram account - you'll see it.
If you mean that in other phones you can add him as a Telegram contact directly, you might want to try and share the contact from one of the other phones with yourself:
If that's the case, it's very weird. I really can't see any reason it would happen.