Connecting balanced (?) cable to unbalanced output from turntable

Hi, I will try to explain - A friend of mine asked me to connect some new phono cables (bought complete with plugs at either end) to his turntable. This involved cutting off the phono plugs at one end and connecting each cable to the tonearm wires. Normally in my experience there is only one insulated core inside each cable and a surrounding ‘ground’ but in these cables were two insulated cores and a surrounding wire mesh. One of the insulated cores went to the inner terminal of the remaining phone plug (on the other end of each cable ) and both the other two wires were connected to the outer terminal. My question is how should these three wires be connected to the connection strip in the turntable which only has two terminals per channel

Hopefully my description in not totally unintelligible and someone may be able to provide guidance. Thanks in advance.

Connect the one from tip of the plug to the original inner core terminal and the other inner wire (that goes to the new plug ground) to the original screen terminal.

Trim the excess screen back just clear of the terminals; it does not connect at the input end.

That style of wiring supposedly gives a better result as the screen is only connected at the amp end, so not taking any current from the signal (or something like that).

I doubt it will make any difference, but it does not hurt anything.

Thanks JRW, that helps a lot.