Old copper bathroom faucet pipe with brass washer

I'm not a plumber, but I have a plumbing problem.
I have a bathroom faucet with a copper rolled pipe... I do not know what to call it, it is probably from 50s or 60s. It runs from the sink knob to the hot water valve and it's covered in green mold(?) on the outside of it, but looks like shiny copper when that crud gets wiped off.
Where it connects to the valve, there appears to be a brass connector, with a brass washer(?) that has some green stuff (putty?) around that washer.
It's definitely some kind of green mold covering the outside of the copper pipe, but the lighter green stuff on the washer looks like some kind of hardened putty.
It leaks where it connects to the hot water valve. Not from the valve itself, but from the hose.
Went to Home Depot and they wanted to sell a new hose. Is this the proper way to handle these old copper pipes? I already disconnected the connection to the hot water valve (the hot water feed where the hot water comes from).
The guys at Home Depot suggested that there's a washer there. I asked them if it's a rubber washer or other. They said you replace the washer by replacing the hose. And I don't see a washer (at least nothing rubber). I see a brass fitting that spins, that appears to have some sort of putty around it.
Thanks for any suggestions.
Jim Carlock

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