Can full motion simulator training time (FSI) be counted towards the required 100 hours that a part 135 captain is a High Minimum Captain?
135.225 - IFR: Takeoff, approach and landing minimums (e) requires:
The MDA or DA/DH and visibility landing minimums prescribed in part 97 of this chapter or in the operator's operations specifications are increased by 100 feet and 1⁄2 mile respectively, but not to exceed the ceiling and visibility minimums for that airport when used as an alternate airport, for each pilot in command of a turbine-powered airplane who has not served at least 100 hours as pilot in command in that type of airplane.
So this means that our question becomes: Can a pilot log PIC time when "flying" a simulator?
The answer to this question comes from 61.51 - Pilot logbooks, where you will notice that none of the bold parts (marked by me) have been met in the situation that you describe. Generally, PIC time requires you to be PIC of an aircraft, and does not provide for PIC time when in a simulator unless you are providing instruction:
(e) Logging pilot-in-command flight time.
(1) A sport, recreational, private, commercial, or airline transport pilot may log pilot in command flight time for flights-
(i) When the pilot is the sole manipulator of the controls of an aircraft for which the pilot is rated, or has sport pilot privileges for that category and class of aircraft, if the aircraft class rating is appropriate;
(ii) When the pilot is the sole occupant in the aircraft;
(iii) When the pilot, except for a holder of a sport or recreational pilot certificate, acts as pilot in command of an aircraft for which more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is conducted; or
(iv) When the pilot performs the duties of pilot in command while under the supervision of a qualified pilot in command provided—
(2) If rated to act as pilot in command of the aircraft, an airline transport pilot may log all flight time while acting as pilot in command of an operation requiring an airline transport pilot certificate.
(3) A certificated flight instructor may log pilot in command flight time for all flight time while serving as the authorized instructor in an operation if the instructor is rated to act as pilot in command of that aircraft.
(4) A student pilot may log pilot-in-command time only when the student pilot—
(i) Is the sole occupant of the aircraft or is performing the duties of pilot of command of an airship requiring more than one pilot flight crewmember;
(ii) Has a solo flight endorsement as required under §61.87 of this part; and
(iii) Is undergoing training for a pilot certificate or rating.