This is probably the genesis of the self-emancipation theory and the role of the USCT:
"The decisive action which ended the Civil War was the emancipation and the arming of the black slave; that, as Lincoln said, 'Without the military help of black freedmen, the war against the south could not have been won.' The freedmen, far from being the inert recipients of freedom at the hands of philanthropists, furnished 200,000 soldiers in the Civil War who took part in nearly 200 battles and skirmishes, and in addition perhaps 300,000 others as effective laborers and helpers.” - W.E.B. Dubois, Black Reconstruction in America, 1860-1880
The Lincoln quote is dubious. As far as I can tell, the only source for it is Dubois. First, it speaks of the war in the past tense, even though there were 150,000 rebels still around when Lincoln was killed. Second, Dubois never met Lincoln. He was born in 1868.
This is an authentic Lincoln quote:
Abraham Lincoln, Washington, DC, December 8, 1863
State of the Union Address
Fellow-Citizens of the Senate and House of Representatives:
…The preliminary emancipation proclamation, issued in September (1862), was running its assigned period to the beginning of the new year. A month later the final proclamation came, including the announcement that colored men of suitable condition would be received into the war service. The policy of emancipation and of employing black soldiers gave to the future a new aspect, about which hope and fear and doubt contended in uncertain conflict.
According to our political system, as a matter of civil administration, the General Government had no lawful power to effect emancipation in any State, and for a long time it had been hoped that the rebellion could be suppressed without resorting to it as a military measure. It was all the while deemed possible that the necessity for it might come, and that if it should the crisis of the contest would then be presented. It came, and, as was anticipated, it was followed by dark and doubtful days.
Eleven months having now passed, we are permitted to take another review. The rebel borders are pressed still farther back, and by the complete opening of the Mississippi the country dominated by the rebellion is divided into distinct parts, with no practical communication between them. Tennessee and Arkansas have been substantially cleared of insurgent control, and influential citizens in each, owners of slaves and advocates of slavery at the beginning of the rebellion, now declare openly for emancipation in their respective States. Of those States not included in the emancipation proclamation, Maryland and Missouri, neither of which three years ago would tolerate any restraint upon the extension of slavery into new Territories, only dispute now as to the best mode of removing it within their own limits.
Of those who were slaves at the beginning of the rebellion full 100,000 are now in the United States military service, about one-half of which number actually bear arms in the ranks, thus giving the double advantage of taking so much labor from the insurgent cause and supplying the places which otherwise must be filled with so many white men. So far as tested, it is difficult to say they are not as good soldiers as any.