According to this instruction, the API in this video doesn't. Not working for the product admins. If I am only the admin of the product but doesn't own the device under the account, the PUT method of this API will return such message: {"ok":false,"error":"Device is not part of this product"}
You can't add a device to a product that's claimed to a developer account that's not a team member. That's by design, otherwise you could just steal any random person's device.
Unclaim the device from the other account before adding it to your product. Normally, you'd add the device to your product before claiming, or not use claiming at all. Using unclaimed product devices is the recommendation now, except for software developers.