The RU lock can accept a Schlage Full Size core, but the cylinder suffix must be specified as "J IC-SC" so the correct parts are supplied. The tailpiece will come with the lock.
Example: RU581J IC-SC
The T lock can accept a Schlage Full Size core, but the cylinder suffix must be specified as "J IC-SC" so the correct parts are supplied (including the tailpiece)
Example: T581J IC-SC
The "C" indicates small format IC core, which is the only core style Falcon products. The C987 will be provided less core unless -6, or -7 suffix is specified (6 or 7 pin core)
Example:...