Cessna 172 pilot reported an elevator flight control malfunction during the initial climb after takeoff while operating under a ferry permit. The pilot returned to land in the opposite direction and Maintenance discovered the elevator trim tab was installed incorrectly.

Narrative

The Flight school I work for requested for one of the instructors to travel to ZZZ to retrieve a 172s and return it to ZZZ1. I volunteered to do the pick up after I finished work in the afternoon and I was planning on completing the flight during the day. Due to delays at work and no further information about Aircraft X; I took off at XA:15 (roughly XX minutes after Evening Civil Twilight). I was informed it was Under a Ferry Permit; but not much else was told to me. I noted the permit in the aircraft but I failed to read the Limitation and notice that it had a Day VFR limitation. Really the only thing they instructed me was to thoroughly preflight the airplane due to not being flown for several months. Weight and balance; Other inspections were looked at but again; I had never dealt with a ferry permit flight and I oversaw reading the Ferry permit itself. That occurrence is one of 2 of the reasons for this report;After a thorough preflight; and no exterior discrepancies were found; Aircraft X experienced what appeared to be a trim or elevator issue that caused the aircraft to enter an extreme nose high attitude. I continued to add nose down trim and I briefly applied nose up trim assuming reverse control malfunction but no change was felt and I did not want to attempt to exacerbate any potential damage. This occurred after lift off from Runway XXR at ZZZ on my way to ZZZ1 in which I had to advise ATC and level off with partial power to reduce tail down force. Highest altitude I noted was possibly between 300 - 400 ft above the ground. I turned back to enter the pattern for XXR but I noticed a consistent loss of altitude with yoke pressure still full forward; a full pattern and successful landing on XXR seemed unlikely; I ended up landing the airplane on XYL. Further maintenance inspections revealed that the trim tab was placed inverted and cables were opposite of the trim wheel movement. The personnel that assembled the trim in this fashion is also the personnel that has said to resolved the issue at ZZZ.