Yes but unfortunately that isn't always how it works. Look for the example with AC's fares to/from Canada and Singapore. AC's fare will book into a mileage earning ticket.. say in Q, or V and the HKG-SIN portion is booked into AC's flight number. But when time came, say 24 hours prior to departure, we really see on SQ's computer that the flight is booked as "V" or "Q" which are non mileage earning.

What is the fare basis of the LH fare? I can try and look it up on how SQ codeshare works out on this ticket.