How to find socket for keyboard connector?
I've dug up the schematics of the T60 keyboard as well as the X41. There is a very high chance that the keyboard receptacle is AA01B-S040VA1 manufactured by JAE. The landing pattern is the same and it looks very much the same (Google images for the 30 pins version: AA01B-S030VA1)  

Molex SlimStack 54363-0478 can be used as a substitute to the AA01B-S040VA1. My previous edits say otherwise because of my bad soldering. After fixing the soldering, it works well.