It should, but there may be space constraints within the case.
You need an available PCIe x16 slot - which the Memphis-S board has
And a PSU capable of running it.
The 1050 is a 75W card - the system has a 300W unit.
https://support.hp.com/ro-en/document/c04397302
The balance of the components should be an i5-4460 (max 84W) and, say ~30W for the RAM, HDD etc
That's a max load of about 190W on a "300W" unit, which probably has 20-22A on the 12V rail (so 240-264W) so should be more than adequate.
I cannot confirm the details of the PSU though. If you had a pic of the labelling on the side of the PSU, that would help.