That's an interesting question. If the part was to stay within the company, then the engineer who removed the part off the U/S engine could sign the tag to certify that it was removed as serviceable. It would then go through the stores system who would issue it with a batch or GRN number. That would allow it to be fitted to the same company aircraft. Similar to a Rob situation.
I don't know how the Form 1 is issued so it would be interesting to hear how that's done.