Yes. Once the war ends, the Raid or War counter goes in the top most spot of the Enemy Instruction Display or if there isn't space there in the Success Draw Cup.
On Page four of the rules states
War Ends: When this phrase is encountered: remove the affected
War Column counters from whatever map space they are currently
situated. Return the Instruction counter into the top-most
empty space on its column of the Enemy Instruction Display (if
all spaces on its column are occupied, place the Instruction counter
into the Success Check Draw Cup). Return its War Column
strength counter to stock.
and right above that it states
War Column: A “War” or “Raid” Instruction counter stacked
with a War Column strength counter in a map space collectively
constitute a War Column.