DS Lite Supercard and Pokemon migration from FR to HGSS

[Htyrohoryth]

I've been looking around for an answer but I couldn't find one that answers my question.

I bought a Supercard not long ago, I figured out saving and I'm very satisfied.

However, besides playing through Pokemon games I want to finish Pokedex in HGSS. My question is: Is it possible to migrate Pokemon from FireRed/LeafGreen to HGSS or D/P/Platinum using a Supercard and R4?
I tried already and the migration option just isn't showing up.
Maybe I should just look for an original cartridge or one of those fake ones?

I'm not interested in trading via emulators or other methods like this unless I'm out of options.

 

[anotherthing]

I believe this might be of help here:

https://www.gamebrew.org/wiki/Pkmn-chest

 

[Htyrohoryth]

I believe this might be of help here:

Unfortunately the app makes my ds freeze and it does not work.