You really don't need to type in all caps, fyi.  But your issue isn't going to be the 1TB capacity.  There isn't a problem there.  The problem is that the 960 Evo is an M.2 NVMe SSD, not an M.2 SATA SSD as you wrote, and the XPS 13 9343 does not support booting from PCIe/NVMe SSDs.  It's not going to work.  If you want a 1TB SSD that will work, you should get the Samsung 860 Evo M.2 SSD, which uses SATA instead.  Make sure you get the M.2 version, since the 860 Evo is also available in 2.5" and mSATA, which won't work in your system.

can you please tell me which ssd worked for you? mine is also same xps 13 9343 now have pm851 128 GB trying for 1TB upgrade.please reply