I recently flew MU JFK-PVG-KUL and back. Outbound posted within 4 days, return took a tad bit longer, but was there within a week of if I recall correctly.
I make sure my Skymiles number is showing in the boarding pass and I keep those until the flights have posted.
At KUL on the return. I used the SkyPriority lane, got the seat I wanted, and boarding passes. But my FFN wasn't showing on my BP. I asked the agent to check and make sure it was there, it wasn't, so they added it.
As long as the FFN is in the pass you should be good. It might not post automatically, but requesting credit should be easy after the flights.