Wiring a flycolor 160a to a bec to the flipsky receiver connector

I had saltwater in my box and the flipsky receiver and the bec are being replaced. I did not do the original build

It is a bec 12s pro. One of the wires to the bec is missing (the input) and I found a random red wire laying connected to nothing this morning and a black ground wire is connected to the bec but not to anything else. I have two brand new connectors that go into the receiver one has 3 wires and one has 4. I think I am using the 4 wire version since my original setup is using a green wire. I am thinking the random red wire is the “in wire” but which wire should it be spliced into?

The input on the bec should connect to the battery red connection and the black ground that isn’t connected to anything should go to the black battery connection?

pictures attached

I am grateful for any guidance as this whole process has been 1 step forward two steps back

I finally got it working again after another snafu and waiting on parts. I tried to replace a bec pro 12s which is what was there. I think I had a bit too much solder on one of the connections so it shorted out. Back to the drawing board. I ordered a Castle Creations CC BEC 2.0 14A Max Output 14S along with a couple of extra flipsky vx3 pro receivers. The new bec comes with wires attached and the two wire connector on it plugs into the flipsky receiver wire. Much better than trying to solder wires to the bec 12s pro. I re siliconed the hole that the wire passes through into the box.
Hopefully this does the trick.