A reader account is its email address, so one person who bought with one address and signed up with another ends up as two: books on one, the sign-in on the other, and neither one whole. Joining them moves the books, the licences and the reading history onto the account they can actually open, and retires the other.
Open Library, then Readers, and press the reader you are looking at.
Merge With Another Account is on the header. It is a Root action - nobody else sees it, and the server refuses it even if the button is reached another way.
Press Merge With Another Account and find the other one.
Search by name or email. The two are then shown as Keeping and Retiring, with the account you opened as the one being kept to start with.
Read what it says would move, under "What this merge does".
That list is not a description written for the help - it is the server's own plan for the merge it is about to run, so the two cannot disagree. Nothing has been written yet.
If it refuses, press Swap.
The reader app finds somebody by the address they SIGN IN with and nothing else, so the account you keep has to be one they can sign in as. The account holding the books very often cannot - a purchase created it and nobody ever signed up - so the refusal names the other address and Swap is the whole answer.
Press Merge These Two.
The books, licences and history move, the retired account is marked as retired, and the kept account takes the earlier first-seen date of the two.
The address that survives is often the WRONG-LOOKING one. If the misspelled address is the one they sign in with, that is the account to keep: a tidier address nobody can sign into leaves them unable to open a single book.
If it refuses because neither account has ever been signed into, there is nothing to join yet. Send them a sign-up link first - see "Readers who have books but cannot sign in" - and merge once one of them exists.