PWK LCL CTLR NEARLY HAS AN ERROR WHEN INCOMPLETE POS RELIEF BRIEFING LEADS TO FALSE ASSUMPTION ABOUT COMS.

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I WAS ASSIGNED TO RELIEVE THE LCL CTLR/CIC AT XA00. AFTER DOING SO; I THEN LEARNED THAT THE RELIEF BRIEFING WAS MISSING SOME KEY DETAILS WHEN C90 APCH CTLR CALLED AND ASKED IF I WAS PROVIDING SEPARATION FROM THOSE 2 ACFT; REFERRING TO A DEP OUTBOUND ON A 030 DEG HDG; ACFT X AND ACFT Y ON A 160 DEG HDG. I REPLIED YES; BELIEVING THAT WE WERE IN CONTACT BY RADIO; AND THAT CTL INSTRUCTIONS COULD BE ISSUED; ONLY TO FIND NEITHER ACFT WAS ON OUR FREQ. THEIR TRACK APPEARED THAT THEY WOULD PROGRESS TO A XING VECTOR; WHICH COULD RESULT IN LTSS. UPON HEARING THE QUESTION; THE RELIEVED CTLR STATED THAT HE MEANT TO GET THE INBOUND TO CANCEL IFR. THAT'S WHEN I LEARNED THAT SOMETHING IN THE BRIEFING WAS MISSING. I CALLED EACH ACFT WITH NO RESPONSE FROM THEM. ALL I COULD DO WAS WATCH AS THEY PASSED. FORTUNATELY; THEY PASSED WITH VERT SEPARATION AND LATERAL SEPARATION HARD TO JUDGE; BUT NO CONFLICT ALERT WENT OFF. NO CORRECTIVE ACTION ON MY PART COULD BE TAKEN BECAUSE BOTH ACFT WERE ON C90 FREQS AT ARR AND DEP.