Italy took over responsibilties for the Caucasus naval operations according to the Weekly Intelligence Summary No. 15 for the week ending 29 March 1919

An item reported that Italy was to become the mandatory power for the Caucasus and responsible for the Caucasus naval operations and preliminary discussions already held. Italian staff officers were underway to the Caucasus to take over from the British staff officers. British troops would leave Krasnovodsk [Türkmenbaşy, Turkmenistan], Petrovsk [Russia] and Baku [Azerbaijan] and to left Trans-Caspia by 31 March.

Source

The National Archives, Kew Gardens, England CAB-24-77-68