The Quaker Finder website has a list of "Frequently Asked Questions" about Quakers. One of the questions is "How Do Quakers View Christ". And part of the answer is
Quakerism is concerned with life in this world rather than the next, and has no theology of heaven and hell. George Fox taught that redemption through Christ and the Second Coming should not be thought of as past and future events. Both can only be experienced in the present, as spiritual truth, independent of history. He believed that "Christ has come to teach his people himself," and that we can be as Adam was before the Fall if we open our hearts to the Inward Teacher.
I have the uneasy feeling that this description of George Fox's beliefs is at best a half-truth. I can see from his writings that Fox said Christ has come to teach his people himself and that we can be as Adam was before the Fall if we open our hearts to the inward teacher. I'm not so sure that Fox ever said the Second Coming "should not be thought of as a future event", though maybe he did, and I'd be willing to find that out if someone can provide a quote. I'd be a little less suprised if the word "only" were inserted into this statement, so that it said the Second Coming should not be thought of only as a future event.
As for the statement that "Quakers have no theology of heaven or hell", I would be astonished if anyone could prove this from documentary evidence. It's almost impossible to prove a negative, anyway, of course. But also it seems to me that there are things scattered throughout Quaker writings over the centuries that seem to indicate an interest by at least some prominent Friends in our eternal destiny.