RADAR CTLR AND COORDINATOR FAILED TO COORDINATE THE VFR ARR OF AN MLT AT AN ADJACENT MIL ARPT. ARR CONFLICTED WITH ACFT IN PATTERN.

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MLT X DEPARTED VFR FROM SHV TO BAD; LESS THAN 10 MI AWAY. ANOTHER ARPT; DTN ARPT; IS LOCATED BTWN SHV AND BAD. THE ACFT CLBED TO 2500' (APPROX 2200' AGL) TO CROSS THE DTN ARPT. BAD IS IN THE ADJACENT SECTOR (RADAR E). BAD IS 2 MI OUTSIDE OF MY AIRSPACE. I SAW NO TFC TO CONFLICT WITH THE ACFT; SO I COORDINATED WITH THE RADAR E CTLR TO KEEP THE ACFT ON MY FREQ AND CHANGE STRAIGHT TO THE TWR TO SAVE A FREQ CHANGE. ENRTE THE ACFT PASSED JUST SE OF THE DTN ARPT AT 2500' MSL. OUR FAC LETTER OF AGREEMENT WITH BAD TWR (A MIL OPERATED TWR) CALLS FOR US TO GIVE INBND ARR INFO TO THE TWR 15 FLYING MILES FROM THE RWY. SINCE THE 2 ARPTS ARE ONLY 10 MI APART; IT WOULD BE BARELY 15 FLYING MILES TOTAL; ALLOWING FOR A 4-5 MI FINAL. THE POS DESCRIPTION OF THE COORDINATOR CTLR FOR MY SECTOR REQUIRES HIM/HER TO GIVE THE INBND INFO TO THE TWR. I SWITCHED THE ACFT TO THE TWR FREQ 4-5 MI W OF THE ARPT. THE COORDINATOR CTLR HAD NOT GIVEN THE ARR INFO TO THE TWR AND I HAD NOT VERIFIED THAT PRIOR TO THE FREQ CHANGE TO THE TWR. THE INBND WAS RAPIDLY GIVEN AND RECEIVED BY THE TWR BEFORE THE ACFT CHKED IN ON THE TWR FREQ; HOWEVER WHEN THIS INFO WAS PASSED; THE ACFT WAS CONSIDERABLY LESS THAN 15 FLYING MILES FROM THE RWY. THE ACFT WAS ON A RIGHT BASE LEG. THE TWR HAD ANOTHER ACFT IN THE VFR PATTERN (MLT Y) THAT WAS TURNING A LEFT BASE. THE TWR ULTIMATELY HAD MLT X BREAK OUT FOR RESEQUENCING. MLT X WAS UNHAPPY WITH THIS OPERATION. THE IMPRESSION HE GAVE ME WAS THAT HE WAS TRYING TO GET TO BAD TO LAND AS QUICKLY AS POSSIBLE AND DIDN'T LIKE THE BREAK OUT (BUT THEN; WHO DOES?). GRANTED; THE TWR RECEIVED THE ARR INFO LATE AND WAS SURPRISED. I WAS QUESTIONED AS TO WHY I HAD NOT VERIFIED THAT THE COORDINATOR HAD NOT COMPLETED REQUIRED ARR INFO TO THE TWR. I GUESS WE BOTH FAILED AS A TEAM. I WAS ALSO QUESTIONED FOR MY REASON FOR ALLOWING THE ACFT TO FLY IN THE PROX OF THE DTN ARPT AT 2500' MSL. I DON'T PRECISELY RECALL EVER HAVING DONE THIS BEFORE; BUT I DID NOT PERCEIVE IT TO BE PARTICULARLY UNSAFE. ALTHOUGH NOT JUSTIFYING THIS OPERATION IN THE VICINITY OF DTN ARPT; OTHER CTLRS HAVE DONE THE SAME THING ON OCCASION. NEEDLESS TO SAY; IT WILL BE A VERY LONG TIME BEFORE ANYONE FROM THIS FAC DOES ANYTHING LIKE THAT AGAIN.