PCB connector to bring out pins on an IC
Seems you have 2 options: 

Option A. Remove the TQFP from the PCB using a hot air tool, taking care not to damage the TQFP by excessive heat or twisting pins. Don't damage the PCB by lifting traces. And don't dislodge other parts that are near to the TQFP. Then solder the TQFP to your 2nd PCB, using a very fine tipped soldering iron, fine solder and lots of flux. Realize that you have soldered the TQFP on the wrong way round, so remove it again using the hot air tool, and solder it on the correct way. Without damaging it. Then use fine wire to connect most of the 144 pins from your 2nd PCB back to the first. If your TQFP has a crystal, any high speed connections or sensitive analog inputs then these quite probably are not going to work correctly now. Even if it does work the whole thing is going to be so fragile that its not going to work for long.

Option B. Use some fine wire to connect directly to the pins of the TQFP.