I do not have access to a Z840 to test with, but here is what I have done multiple times with the xw6400 xw6600 Z400 Z600 and Z620 workstations:
I use a bootable Acronis True Image CD or USB to capture a clone image of the W7Pro64 install from the boot HDD, and restore to a freshly NTFS formatted SSD from the image (which is on an external eSATA attached drive). These are not RAID builds.... they are single boot HDD with documents HDD also in place, to start with. The HDD and subsequent SSD clone build is running under latest BIOS from HP, and the OS install has been properly created by HP (from factory) or by me, both having the small "system reserved" partition properly present. You can see that under Device Manager\ Disk Management.
If there is a HP Restore partition on the HP HDD I capture that also in the process, and that gets transferred over to the SSD and is still usable (unless it has already been used).
I'm preferring only Intel SSDs, and if the workstation was a SATA Gen II one I use Intel SATA Gen II target SSD. I run BIOS in Legacy mode. SATA emulation is always set to RAID + AHCI. I use the Intel ToolBox SSD software to fine tune the SSD after install.
The Acronis method I am using will automatically upsize or downsize the OS HDD clone to the SSD. That is, if the HDD has less data on it than the SSD is in size the process will work. That image can be used to clone onto another SSD in the future, so if the build is from HP the HP OEM COA will work on another same-type workstation. If it is one of my builds from a System Builder DVD with unique COA then the clone to the same workstation will work fine under that COA, but to another same-type workstation I'll need to feed it another COA within 3 days.
A 500GB boot HDD will clone over to a 160GB SSD fine if the amount on the HDD is less than 160GB. I generally now am using at least 300GB SSD, and you want to leave about 20% of a SSD unused for its best utilization.
I have been doing this for over 2.5 years, with no issues at all. This is in an enterprise environment, and also at home. I know some other posters have said it cannot be done, but it is working well for us.