Yes. do away with the solenoid on the firewall. The battery cable should go from the battery to the large stud on the starter, then relay a smaller gauge wire (8-10 ga) from the large post on the starter to the stud on the back of the alternator. You will want to extend the small wire that was on the solenoid on the firewall (ignition) and run it to the small stud on the back of the new starter. (unless your new wiring harness included that wire) You can run another 10 ga from the back of the alternator to the fuse block. You will want the computer to be on the igniton switch source. good Luck.
On a side note do not forget to run the battery ground straight to the block, then run a ground strap from the block to the frame.
1989 Islander 4.2 Automatic. RC 2.5" lift. 265/75/16