If an elf and a half-elf (let's assume the elf and the half-elf's elven parent are of the same subrace, to exclude that complication) were to have a child, would the child be an elf or a half-elf?
I can see this going either way; one argument might be that the child would be an elf because between the parents, there's 1/4 human and 3/4 elf, but on the other hand, "the child of a half-elf is always a half-elf" is the sort of thing I wouldn't be surprised to see somewhere.
However, I cannot find anything to support either conclusion in the PHB or XGtE or anything.
Is the offspring of an elf and a half-elf an elf or a half-elf? Does any official lore support one of these conclusions?
Different settings might have different answers to this question, so let's make this specific to the Forgotten Realms. Since this is relevant to a 5e game, ideally the answers should come from 5e, but I'll accept lore from previous editions, so long as it's Forgotten Realms.
Best Answer
XGtE suggests that you are free to make it up.
Ideas, not rules (XGtE, 61):
The Nonhuman Parents table (XGtE 62) shows that it is possible for a half-elf's parents to be both an elf and a half-elf:
So it confirms that that half-elves and elves may have half-elven children, but that you are free to decide either way. As 5e lore doesn't go into more detail you may borrow inspiration from other editions if you do desire to do so.
3.e says (Races of Faerûn 58):
2e says (PHB 30):
(AD&D 2e) Forgotten Realms Campaign Setting Box Set Revised p. 12 phrases this more concise and less ambigious:
These older editions strictly denote that elves have only elven ancestors, that means at least one parent has to be a full-blooded elf to give birth to an elf when mating with an elf or a half-elf, but no such restriction is a confirmed part of the 5e lore.