"Leanfaidh sé ar aghaidh leis an leabhar."
Translation:He will continue on with the book.
I do not believe that "continue on" is a normal phrasal verb (at least in American English) — usually just plain "continue" would suffice. There is the phrase "carry on", however — might this not be a better translation of the intended meaning here? Of course "carry on" has a second, totally different sense too.