Perhaps I can help with this.....
A 3.5" hard drive has its rear SATA data and power ports shifted to the side, when viewed from the rear. Most 2.5 to 3.5" form factor adapters do not shift things to the side to the correct amount.
The Z620 drive drawers slide in on rails, and if a 3.5" HDD is in place in the drawer it meshes perfectly with a rear device called a BlindMate receiver, made by Foxconn for HP.
So, to get a 2.5" form factor SSD to mesh perfectly with that you need a proper 2.5 to 3.5" adapter, not some generic adapter.
My two favorites are the Western Digital IcePack, and one made by Foxconn for HP. Go to eBay and search for:
1. WD Icepack, and get the one with ribs going the way showing in the pic below. You can pull off the gray foam, and the SSD screws in from below:
2. This is the one I actually like the best, and it is a HP product. The screws go in from the side rather than from the bottom, and here is the part number to search for on eBay... 654540-001. Here is a pic:. When you screw your SSD into this adapter, and then fit the pair to the Z620 drawer, you'll be able to slide the drawer into its receiver and the drive will be physically mounted perfectly.
Then, there is the issue of whether you have a drive that is properly NTFS formatted and of the MBR type of initialization ahead of time. If you don't understand that then you have some homework to do:. If you already have the SSD NTFS formatted and showing up on a Windows workstation via some other connection then I bet you just need the right adapter to get things to physically mesh together properly. Here is that pic of the HP adapter:
