You have a nice collectible there. Unusual to have a check - you commonly see stamps (not real common - but you don't see checks).
The purpose was to regulate coal during the war and insure that the military got what they needed and then civilians could get it at a monitored rate.
(These are also the Bozos that created Daylight Savings Time - they ruined my great hiding places when we played hide-n-seek at night as a kid - because at 8pm when it was light it was harder to hide!
Can you please post a picture.
Most likely a reimbursement check. Was he employed by them?