I am a citizen of the Philippines who is a permanent resident in Ukraine. I was granted a 10 years multiple entry visa in 2019 by the Embassy of Mexico in Ukraine. Embassies are busy this week relocating their citizens due to a possible Russian invasion according to the USA intel. Hence, I decided to just email the Mexican Embassy and here was their reply:
Hence, as long as the Mexico multiple entry visa is valid, there is no need to transfer it to the new Philippines Passport. You must just present your old passport with a valid Mexico visa and your new passport to the Mexico immigration control at the country’s arrival area.