Hi @teddyalemu
Looking at the SSD parts list (Item #13 p.20) of the [http://h10032.www1.hp.com/ctg/Manual/c07067670.pdf|maintenance and service guide] taken from this support [https://support.hp.com/us-en/product/setup-user-guides/hp-elitebook-835-g8-notebook-pc/model/2100108645|webpage] for the laptop, the laptop supports PCIe M.2 SSD usually NVMe.
M.2 cards can be [https://www.partitionwizard.com/partitionmanager/m2-m-vs-bm.html|keyed] either as M or B or both
All the SSDs listed for the laptop are M keyed NVMe i.e. PCIe.
Your SSD is a sata M.2 and images show that it is B+M keyed so it will insert OK but this doesn't mean that it will work. It depends on the motherboard design.