Bonjour to our French friend!
Your Z620 is almost certainly a version 1, but please do check in BIOS for its boot block date. Some version 2 motherboards may have been sold with that processor in place. The version 2 motherboards can run all the older processors, and the newer ones too. That would be worth knowing.
By looking at the early QuickSpecs for the Z620 you can see the different processors that HP certified for the version 1 motherboard. For example, look at version 5 of the QuickSpecs from May Day, 2012, HERE. There you can see that your original "E5-1605" is not listed.... are you sure it is not E5-1650, which is listed? You can see that the processors you want to use are there..... E5-2640. Note that if your computer came with a E5-1650 you have a heatsink/fan that is rated for 130W max TDP. Look at the E5-2643 instead of the E5-2640.... it is a 130W processor, runs its memory at 1600 Mhz rather than 1333, and has QPI speed of 8 instead of 7.2. So, do you need 12 cores, or 8? And, a clock speed of 3.3 GHz instead of 2.5 GHz? I'd go for less cores and faster, personally.
This all is about the fine tuning of your workstation. If you already have 1600 MHz memory that is another way you would benefit from choosing the processor that is faster with less cores. The slower processor will drop your memory speed to its own, automatically (1333 MHz). You're adding a significant number of cores with your second processor. Perhaps balance that with less cores and more speed of each core?
But, your choice of 2 x E5-2640 is certified by HP for use in the Z620 regardless if you have a version 1 or version 2 motherboard. Plus, from the Intel Ark site it has 2 QPI links, and thus will work in a 2 processor install. Same with the E5-2643. Then, if you look up in the Ark site the sSpec code there is only 1 for the E5-2643 (SR0L7) and 1 for the E5-2640 (SR0KR). That means you don't have to worry about buying the most recent sSpec code... there is only 1 for each processors. Some others have 2 or even 3.
New from Intel Used from eBay
E5-2640 $885 USD about $32 USD
E5-2643 $885 USD about $115 USD
This is one example of how you can zero in on what to buy..... the market says that E5-2643 is a better processor for you if you can budget for it. I searched eBay using the sSpec codes provided above....