Are they partners or what?

Here is an interesting process problem I discovered when trying to check into my flight home from Singapore.   Lufthansa and Singapore Airlines are both Star Alliance, so they code share.  My Singapore to Frankfurt flight was Singapore Air and my Frankfurt to Boston was Lufthansa. But I bought the whole ticket from Lufthansa (on their site) and the flight numbers were all listed as Lufthansa.  But when I went online to check in, Lufthansa knew I was going Frankfurt to Boston and let me print out that board pass.  But they had no record of the Singapore flight.  Then I logged into Singapore Air’s web site and they had no record of it either.  So I could print out my second boarding pass, but not my first one.  I had to do that at the airport.  Very weird.  In Boston on my way to Singapore, I used the Lufthansa kiosk and it let me print out both.