Merit badge counselors are council or district positions so they should appear in the Merit Badge Counselor List search visible to unit leaders on the unit’s page.
A unit leader can also see adults in their unit that are merit badge counselors by going to their Roster and selecting Print Roster.
Merit Badge Counselors can see their position by logging into Scoutbook, click on My Dashboard >> My Positions.
They will not show as having the position on the troop roster because it is a council position, not a troop position. However the troop admin can see them when they print the unit roster and ask for a listing of merit badge counselors.
The counselor should also show up in the Merit Badge Counselor search on the troop page.
The council admin should see the counselor in the Merit Badge Counselor list on the Manage Approved Merit Badge Counselors page.
If there are still issues, check to make sure the member ID in Scoutbook is the same as they have in their registration as a MBC and that their youth protection training is up to date.
If needed, a Council Registrar can push a MBC to Scoutbook by going into their MBC record in my.Scouting and expiring the MBC; wait a day, then add them back.
There is also a merit badge counselor list available to district and council members here.