Can a reviewer suggest literature for improving the language? I am working on my PhD now for 1.5 years and was recently asked by my supervisor to assist him with a review. The reviewed paper was also written by a non-native speaker.

For my first publication I bought a book on English writing skills for research papers, which was very helpful for me.

Can I suggest this book to the author of the paper I got for review, so he can improve his English? I do not want to critize him, only to give him an advice I also give my colleagues.
I am not sure if this exceeds my responsibility.
Certainly, poor English is a significant problem, one that hinders communication, and undoubtedly has an impact on one's ability to publish top-quality articles.

It may sound a bit rude to make such a suggestion, but in extreme cases I think it is warranted. It's probably better and more cost effective than trying to improve the English yourself and better in the long run than  simply ignoring the problem (and suggesting to reject the paper).