Travelling without Canada permanent residency card

A Canadian permanent resident who wishes to return to Canada and does not have a valid permanent resident card can apply for a permanent resident travel document.

Attempting to enter as a visitor is unlikely to succeed because, as a German national, your boyfriend needs eTA authorization to fly to Canada, but, like Canadian citizens, permanent residents are not eligible for eTA:

Travellers who cannot apply for an eTA and need to carry other identification:

• Canadian citizens, including dual citizens, need a valid Canadian passport. American-Canadians can travel with a valid Canadian or U.S. passport.
• Canadian permanent residents need a valid permanent resident card or permanent resident travel document.
• Visa-required including alien’s passport holders and stateless individuals.

Another option would be to return to North America through the US using the visa waiver program and then drive across the border to Canada. See I need to leave Canada and I do not have a permanent resident card. Can I later return to Canada without a PR card?

Don't panic! Your boyfriend can simply get a Permanent resident travel document. It allows a single entry into Canada for PR folks without their PR Card for whatever reason. I think (but check the link) you need to go to an embassy for this - if you are near Berlin there is one there.

(PS I am a new PR but had to leave the country before my card arrived. This was the route immigration recommended for me).