I thought I might be able to find these people in Sidney Perley's Plumer genealogy, but I didn't.I feel it is very likely that if you can get back another generation or maybe two you will be able to pick up from there in the book.I would guess that a Plumer in Portsmouth is almost certainly a descendant of Francis Plumer who came to Newbury, MA, ca. 1630.
If you do have information further back, and it doesn't sound as though you do, I'd be happy to check the book.I did find an Albert and Charles B. "pair," but too early and in the wrong order.This could very well be your Albert and his father, but there's no way I would know.There is very little information on these people in the book, and Albert's birth date is not given, but his siblings Lorenzo and Augusta were born in the 1860's and the LDS file on your Albert has an estimated birth date of 1866.These people lived at Durham, which is just across the bay from Portsmouth.
I don't know what you have tried so far. I think if I didn't know more than what you have mentioned my next step would be to find my local Family History Center (which would be listed at the LDS website) and see if they have the new 1880 census CD that the church has just put out. I believe it is all name searchable, so one should be able to pick up Albert. If you can find a likely Albert who is somewhere in his teens or even early twentiesthe 1880 census should have a good deal more information.Assuming that he was living with his parents you ought to be able to move easily from there--I would expect the Perley book would be of use from that point.My local FHC is closed for August or I'd check it for you.Another possibility is to try the Rootsweb Rockingham County NH mailing list and see if anyone can help.
My mother's mother was a Plumer from Portsmouth.I checked our bible records and didn't find anything, but maybe we have a connection somehow.
Good luck, and please let me know if you get to a pointwhere the book might be helpful or if it gets to be Sep. and you haven't been able to try the 1880 census.Also I looked at what microfilmed original records are available for Portsmouth through LDS and they don't have VR for the period of interest, but there are some church records.Plumers would likely be Congregationalists, so the Church of Christ records might possibly help--but I'd try the census first.