Thank you for your answer, that's interesting.
If I throw away the half of FMM I have now while inside Mexico, the INM system definitely thinks that I am still outside of Mexico (since I flew out of Mexico and "checked out" officially at an INM counter in the airport), then I have other questions coming up in my mind:
1. When it's time to renew my "green card" in an INM office, will they deny renewal since their system hasn't checked me in ?(I assume that there is law to require the applicant to be physically in Mexico to renew?) , so do I have to make a special trip out of Mexico and come back by plane or other ways where I have to see an INM officer to check in ?
2. If I decide to fly out of Mexico with my current "green card" before renewal, will I need to pay a fine or will it cause any trouble, since I didn't check in then suddenly I am checking out again in the airport.
Thank you so much for reading my questions again, any thoughts or first hand experience will be highly appreciated