I was able to test it now and finally it worked!! I'm so happy! Thank you so much for your help!
In terms of legality: Well, since my way to obtain it includes cheating, it's not "legal" anyway. But what exactly do you mean? Does the game (FireRed in my case to which I transfer it) understand or notice that this Mew can't be legal or is cheated? Or do you mean in terms of competition? Since I only play Gen 3 for myself, it won't affect anybody/anything else but me and my game save
I was playing Gen 1 and 2 back when they were released and Mewtoo and Mew were always my favourite Pokémon. Now I started my brothers' old cartridges to relive that experience on my old GBMicro and I was quite unhappy that Mew can't be caught in Gen 3 as "easy" as it was in R/B (till now). My goal at the moment is to have a legally completed game save on FireRed (Kanto-Dex for now, maybe Johto later) but since Mew can't be caught, I decided to make this one cheat-exception (let's see though... if I decide to catch the remaining 100 Johto-Pkmn, I guess I will have to do it again for Ho-oh, Lugia and Celebi).
I also have HeartGold with a legally obtained Mew from around the time it was released but will play that after I finished Gen 3