Hello,
Thank you for posting in Q&A forum.
In general, Microsoft's Unified Receiver software does not support pairing devices with different models or serial numbers to the same receiver. Although your two mice are from the same model, they may have different serial numbers or identifications, so pairing the new mouse with the old receiver may not be successful using the Unified Receiver software.
If the device you purchased is missing a USB receiver, you may want to contact the seller to see if you can get a replacement receiver.
I hope the information above is helpful.
Best Regards,
Yanhong Liu
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