The treaty is absolutely clear.If the sub is buils outside the Black Sea it is allowed to travel where and when it want.
This shouldn't be so hard.Montreux Convention Article 12. wrote:
Black Sea Powers shall have the right to send through the Straits, for the purpose of rejoining their base, submarines constructed or purchased outside the Black Sea, provided that adequate notice of the laying down or purchase of such submarines shallI have been given to Turkey.
Submarines belonging to the said Powers shall also be entitled to pass through the Straits to be repaired in dockyards outside the Black Sea on condition that detailed information on the matter is given to Turkey.
In either case, the said submarines must travel by day and on the surface, and must pass though the Straits singly.
Worse, we discussed this at length previously.