Whatever happened to Scrooge’s partner after he gave his warning about the three ghosts? I know it’s way before Christmas, but I just have to know! It just seems strange to me that he’s never mentioned again in the book. Granted in at least one publication he was redeemed severely at the end of it, but it was ONLY one publication and a magazine at that, so that publication probably isn’t canon.
There is no textual answer to this question. Instead, however, we can perhaps artifice one by looking at the religious beliefs of the author.
The academic symposium The Dickens Project has this to say on the subject of Dickens' religion.
In all his writings, Charles Dickens—a Christian of the broadest kind—is outspoken in his dislike of evangelicalism and Roman Catholicism
Dickens's parents were Anglican, but evidently entirely uninterested in the dogmas of the Church of England and probably not very regular in their worship.
So, while Dickens was not evangelical and was actively critical of aspects of religious life, he was certainly a believer. While he was disinterested in dogma, those beliefs were broadly Anglican and Protestant in nature.
This is important because some Catholic doctrines believe in the existence of purgatory, a place between heaven and hell. Those who die outside of a state of grace may go there and hope to redeem themselves and enter heaven.
But Dickens rejected Catholicism and so we cannot imagine that he envisaged Marley as residing in purgatory. It's also clear that he cannot be in heaven, due to his sins. He must, therefore, have come from hell.
But if Dickens was not particularly religious, would he have cared about this at all?
It is evident at the time of his first American trip in 1842 ... It was in these years too that Dickens first felt the need to impart some religious instruction to his children and, significantly, undertook to do this himself by writing a simplified version of the gospels designed for reading aloud
A Christmas Carol was written in 1843 which, we may infer, was at the height of Dickens' religious feelings. So it seems likely he at least dwelled on the theological possibilities of Marley's fate. Given that he is in hell, and there is no redemption from hell, it is tempting to conclude that there is no redemption for him.
Although Dickens mentions Christ's coming again "to judge the world" (LOL 11), he seems never to have taken seriously the possibility of eternal damnation and is always bitterly critical of the harm done by those who hold out the threat of hellfire, especially over the young.
Now, if Dickens was broadly religious, there is no suggestion that he did not believe in hell. We do, however, know, that he was disinterested in dogma. Therefore this statement has to be interpreted as his believing, contrary to doctrine, that sinners could be redeemed from hell.
So it seems that we can imagine a kinder fate for Marley after all. Having paid his punishment and assisted Scrooge, Dickens might well have believed that Marley could eventually be redeemed.
EDIT: I re-read the story over Christmas, and found the following relevant passage.
"It is required of every man," the Ghost returned, "that the spirit within him should walk abroad among his fellowmen, and travel far and wide; and if that spirit goes not forth in life, it is condemned to do so after death. It is doomed to wander through the world -- oh, woe is me! -- and witness what it cannot share, but might have shared on earth, and turned to happiness!"
The Ghost in question here is Marley. So it would seem that instead of hell, Marley's haunting in heavy chains is the punishment given to him for his sins. He implies that this is a fate shared by others too.
This would fit with Dickens' rejection of eternal hellfire and adds weight to the supposition that Marley might have been freed some time after his encounter with Scrooge. Although Jacob also says.
weary journeys lie before me!
So perhaps he has more punishment to pay yet.
Reposting Joshua Engel's comment as an answer:
The impression I get is that because he's dead, he's unredeemable. The point is that Scrooge has to mend his ways before it's too late. Conceivably he gets some kind of bonus points for taking the trouble to appear to Scrooge, but he doesn't really have a story arc here. He's just deceased.