Wikipedia indicates that the official Union reports of the raid have never been found, but at least one newspaper account from a pro-Union paper says that the commander of the regiment, Col. James Montgomery "was followed by a speech from the black woman who led the raid" (obviously Tubman).
Although Wiki is correct in not find Montgomery's actual report I did find the following in the OR's
HEADQUARTERS DEPARTMENT OF THE SOUTH,
Hilton Head, Port Royal, S.C., June 3, 1863. s1 vol XIV (S#20) pg 463
Hon. E. M. STANTON,
Secretary of War, Washington, D. C.:
SIR: I have much pleasure in transmitting to you herewith certified copy of a telegraphic report(*) just revived from Col. James Montgomery, commanding Second South Carolina Regiment, of the result of the first of a series of raids upon the main-land, now organized and in process of being carried out.
From the report you will see that Colonel Montgomery, with 300 men of his regiment and a section of the Third Rhode Island Battery, commanded by Captain Brayton, penetrated the country of the enemy 25 miles, destroyed a pontoon bridge across the Combahee River, together with a vast amount of cotton, rice, and other property, and brought away with him 725 slaves and some 5 horses....
D. HUNTER, Major-General, Commanding.
(*) report not found
Nothing is noted by Hunter of anything about Harriet.