Your question is a bit unclear. In order to sponsor your boyfriend for PR, you must either be married or you must be common law. Common law means you have lived together for at least one full year continuously (and can prove it). Information on how to sponsor him for PR once you meet these requirements can be found here:
http://www.cic.gc.ca/english/information/applications/spouse.asp
Once he is officially a permanent resident, yes, he can take courses to complete his high school education here.
If he wants to complete high school in Canada before he becomes a PR, then he will need to apply for a study permit and will need to be prepared to pay tuition of $15,000 per year to attend public high school in Canada (private school will cost more).
