ZHU D-Side controller described event when both he/she and the RADAR controller failed to properly coordinate an arrival with VCT tower which resulted in a potential conflict.

Narrative

I was moved onto the VCT d-side to help out. Numerous aircraft were inbound to VCT airport for practice IFR approaches as well as VFR flight following to VCT airport for pattern work. I manually passed inbound information to VCT Tower on several IFR aircraft inbound. Aircraft X was vectored for sequence behind a military training aircraft. Once separation was assured; Aircraft X was cleared inbound to VCT airport and cleared for a visual approach. Later; near the VCT VOR; Aircraft X asked about traffic near him. The R side said there was numerous aircraft in the VCT pattern VFR and that the aircraft Aircraft X was seeing was talking to VCT tower. The R side then put Aircraft X on the VCT tower frequency. Recommendation; the R side forgot to put Aircraft X on the VCT tower frequency; and I failed to notice. Perhaps not having to manually pass inbound information to VCT tower; as well as give tower full departure clearances would lessen the workload at this sector. Redesign of sector 58 (VCT) to accommodate vectoring for approach at VCT airport on something less than a 115 NM range would help. Adapting the radar configuration to allow the use of 3nm separation is possible there too. Another idea would be to mark a ring around VCT airport where by LOA we're supposed to put IFR aircraft on the tower as a reminder.