Hello,
I bought a laptop today - ThinkPad Edge E530 (model: 3259D8G)
[i3-3110M(2.4GHz),4GB RAM,500GB 7200rpm HD,15.6in 1366x768 LCD,Intel HD Graphics,CDRW/DVDRW,Intel 802.11bgn wireless,Bluetooth,1Gb Ethernet,UltraNav,Fingerprint reader,Camera,6c Li-Ion,No preload OS],

I noticed the underside of the flap mSATA connector.
Is this computer (the socket) handle mSATA hard drive Plextor M5M PX-128M5M (128GB) or PX-64M5M (64GB) ????

I don't see a reason why it would fail to work.

I do not know why I'm asking I want to make sure you do not buy the disc and be disappointed that it will not work.
E530 Controller mPCIe the mSATA mode controller is connected to a SATA II (3Gb / s) and yet M5M Plextor drive is the drive on the interface SATA III (6Gb / s). So here I am afraid that there may be some incompatibility.
Besides E530 models are configured Intel Rapid Storage slot that is in the mSATA drive is but a capacity of only 16 or 32GB.
So hence my concern or 64GB or 128GB drive will begin in the notebook.

There are no compatibility issues with SATA II & SATA III. They are backwards and forward compatible. It will just run the drive at SATA II speeds, which is still a huge improvement over the 7200rpm jackhammer. There are also no issues with capacity. There is no reason why it would not work.