A Mechanic reports he inadvertently reinstalled the same APU fuel flow divider; he had just removed from a B757-200 and labeled the new serviceable part as unserviceable. The unserviceable parts list showed the serviceable part was never installed on the aircraft.

Narrative

I was working a B757-200 and I removed an APU fuel flow divider from the APU; at approx XA:30 local time. Reinstalled the old part on the APU engine in error. Taking the serviceable part in error; as the unserviceable part; and documenting the error on the unserviceable parts tag and log page.This event happened on Pad 5 at the hangar. I was the one involved in this incident. The unserviceable parts list shows the serviceable part was never installed on this aircraft. I documented the removal of the unserviceable part the same as the serviceable part serial number.I was working the B757-200 in a very dark lighting; (tail of aircraft). I set down removed old part on the tool storage lid; (normally used for a bench) and removed fittings and O-rings; to install on new part. However; I was complacent and installed fittings and O-rings back on old part. The old removed part was reinstalled; in error.Supervisor informed me about this error of part information of an APU fuel flow divider. Going through maintenance parts history; we realized for sure the new part was never installed; and the old part remains installed on the aircraft. The B757-200 was reported by Line Manager; to be arriving early morning for an outbound flight. Maintenance Control notified by Supervisor of the situation of the part discrepancy. I would; that I pay better attention in this situation of dim lighting.