Yes, i know what "drain" wire you are speaking off. It's not too clear in the pics but its definitely there.Yes, that looks like shielded cable.
There should be a thin "drain" wire - an unjacketed wire running along with the foil shield. Connect the outside of the phono plug to this and the inner to any one of the other cables.
Being a big newb can you clarify what type of Phono Plug are you talking about? Is that basically an RCA adapter? My results for phono plug adaptor is varying quite a bit.