A11 Controller described a near loss of separation when a fellow controller requested aircraft be transferred to his/her sector on opposite base track; at the same altitude; resulting in a vector through the LOC to secure separation.

Narrative

I was working South Radar and was feeding my Final Controller. Weather was IFR and everybody was conducting the ILS Approach. North Radar had an airplane (Air Carrier X) B190 on a left base for final. This aircraft was talking to Final Radar and was at 3;000 FT (as per our facility order). I; South Radar; had an Air Taxi Y B190 that was at 3;000 FT and I asked the Final Controller if a heading of 320 degrees would be acceptable. As a 340 degree heading would put both airplanes on converging opposite bases at the same altitude; Final Controller said 'No; put him on a base.' I then replied that Air Taxi X was also on an opposite base at the same altitude. Final Controller didn't want to change the sequence. I then put the Air Taxi Y on a true base leg; 340 degrees and shipped the aircraft to the Final Controller. About 2 minutes later; I noticed that the Air Taxi X aircraft had not received an ILS approach clearance and that the Final Controller forgot to clear the aircraft. Final Controller was late on doing so. Final Controller cleared the Air Taxi X through the LOC and immediately turned the Air Taxi Y aircraft to a sharp left turn to avoid a conflict.