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What procedure did you follow? I was able to program a genie GDO. You have to use the GDO's handheld remote to program the in car transmitter, then program the GDO when in learn mode.
For our old school cars you need to grab a Liftmaster 855LM Chamberlain bridge. It plugs into a garage outlet - find a video to set up. But set your unit to that opener, then program that to your older legacy car homelink and it works fine.
I grabbed some Command velcro and stuck the bridge door opener to the box so I dont lose it :-)
Good advice from @biacs : garage door openers changed aroutnd 2010+ for added security. The old car-based openers (homelink?) don't work with newer receivers. I just use a 2-button opener in my LS430, as the 2 doors are matching brands, and i don't really care. But bridge is alternative.