It has been shown on here that none of the unique doctrines of the WT/JW religion come from Charles Taze Russell, so the present Org. has no theological connection with him.
The historical connection with him is really a fiction too, what Joseph. F. Rutherford did was seize control of the WT Corporation, and ownership, and the chief writer and editor positions, of the Watchtower magazine.
As soon as JFR got the power he started to sideline Russells work, he had to be subtle, those that had supported his coup were still in thrall to CTR, and their support was not without its reservations for Rutherford. He advocated straight away that congregations study together the Watchtower magazine, rather than Russells writings, which could be read at home.
This way all the Bible Student Congregations that remained affiliated were reading the thoughts of Rutherford alone. Straight away he claimed that "The Society" was God's Sole Channel and anyone outside the movement could not be saved. He had started his very own cult.
So, the question arises, why does the WT continue the fiction of a connection to Russell ? As has been shown, Russells ideas were not really his own, so if the interest was to truly show the growth of the modern movement from its start they would have to go back further than him.
C.T Russell was it seems loved by many and respected by even more, preachers of other denominations even compared him with other great preachers who had gone before, Spurgeon and Moody etc . So could it be that the WT likes to maintain the connection with CTR as a much more cuddly figure from history than Rutherford ?
Identification with Russell has not been without its problems, but can you imagine what it would be like if the JW's claimed that the modern movement was started by Rutherford, and the spotlight was therefore put upon him ?
That would be disastrous, so, what is essntially a fiction, the Mantle passing down from Russell is embraced by the WT as the lesser of two evils, and to draw attention away from Rutherford, and they get away with it, because until you look closely it seems to be true history.
As with most of the WT's claims, it is far from the truth.