WILL BEST SFIC FIT IN FALCON X-SERIES LOCK?

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ND locks can be extended up to 6" Extended Outside.  
Schlage does not have a stainless steel/non-ferrous lock series. The only option that Allegion provides is the Grade 1 cylindrical Falcon X-Series. To order the Falcon X with the stainless st...
The Falcon MA will not fit a 1-3/8" thick door. 
The B600 (standard cylinder only) can be be specified for 1 3/8" thin doors and the appropriate parts will be supplied.  Interchangeable cores are not available for 1 3/8" thin doors.
The outside housing, B600-089, can be ordered to retrofit an existing standard cylinder B600.   Description: 1 1/8” Collar (trim ring) for 1 3/8” – 1 5/8” door
The L Series lock can fit into a door prepped for the SCHLAGE K Series with some additional prep as described here.  
K and L trim and parts are not interchangeable. 
The Schlage B and BD cylinder suffixes designate less small format interchangeable core (SFIC) cylinder prep for the lock. Any SFIC, 6-pin or 7-pin, can be inserted into the lock and will operate t...
The B series accepts 6 or 7 pin small format cores when specifying with the "BD" cylinder suffix (less small format interchangeable core).  The tailpiece shown below is used for bo...