MCI Controller described Class B incursion event that required intervention to maintain separation; reporter indicated that preceeding MCI Controller may have issued Class B clearance.

Narrative

While working Arrival RADAR; I noticed a VFR target from the MKC airport area climbing northwest bound into the Class B airspace out of 3;000 FT. Tagged target with Aircraft Y and observed it climbing up to 3;500 FT; still northwest bound. I had Aircraft X on vector to final Runway 1L at 3;000 FT; MKC called and advised they were talking to aircraft and descending. I advised them that aircraft needed to descend fast; I had Aircraft X on vector to join final. I observed Aircraft Y to turn southwest bound toward my Aircraft X; I called traffic alert and vectored Aircraft X away from target and then back to final north of Aircraft Y. Aircraft Y continued southwest bound and descended below the Class B airspace toward LWC. Advised FLM (Front Line Manager); who called and talked to MKC and got the aircraft call sign and possible destination. Recommendation; it appeared MKC gave aircraft a discrete code; if this is true; then MKC should always add in with code to remain outside of Class B (which they might do). If aircraft was not on discrete code then they should try to advise VFR aircraft to remain outside of Class B.