Rewiring a kohler cv14s

I removed all the wiring and have got this setup so far I have a 4 post solenoid on the two big posts I have the positive battery cable hooked up and on the other side is the starter cable. On the two small posts one is a ground and the other one goes up to the key switch. As of right now it starts great but I don't have the charging system hooked up could I just simply take the hot wire from charging cool and connect it to the same solenoid post as the battery and then backfeed power into the battery and charge it up? I have never wired anything in my life so getting it to start was a bug achievement so any help is appreciated

Assuming the wire in question is the charging circuit, yes, it is perfectly acceptable to connect it to the battery post on the solenoid.