The connectors do not need to match the brand of hardline, but they must be sized correctly. The connector you showed in your picture (L5NF) was made by Andrews. The L5NF is no longer manufactured, but I would think they make something similar. I don't know if it could be reused with the correct preparation, but it looks like it might be an N female, rather than N male. It looks like someone used it with a jumper of coax, possibly something like LMR. I know some people are against using LMR400 for repeaters because it has two different shield metals. If you subscribe to that theory, get M&P Ultraflex 10 jumpers; they are copper for all layers of shielding.
So, with the connector you have, with N female on the ends (male thread on the outside, but a female socket on the inside) you would use an N male to N male coax jumper. A short jumper of M&P Ultraflex from Gigaparts will work well.