Can't you just say "Hun sluttet å lese bøkene" ? I fail to see what semantics the "for" brings.
Noun definiteness aside (the Norwegian sentence uses the indefinite plural), the preposition is the difference between "She stopped reading books" and "She stopped in order to read books".
This is more an english question but why is "She stopped to read books" incorrect ?
Because that would mean that stopped doing something else in order to read books.
'lesning' is used as part of a word -> forelesning, gjennom lesning. If you just use 'lesning', it's used differently -> Rapporter er ikke en enkel lesning -> The report is not an easy read. Does that help?