There is video tutorials on youtube, I think you first need to extract the save data from ps2 memory card, you need some card reader for pc or homebrew ps2 with free mc boot installed on the memory card with a way to transfer to pc, then use a pc tool to convert it to work on ps3. But remember there to formats on ps3
One is for ps2 Disc on backwards compatible hardware, and the other is for playstation store installed format. One is created by system menu and called memory card, which works with ps2 format disc, the other only works with the installed game and nothing else can be managed on it. IS almost the same as ps4 ps2 games, only the game will read the data, is not shared is specific. Ps2 format disc data use a memory card that can be used with multiple games to save on singe memory card while installed games will create 2 memory cards and only the game can work with it. Maybe game faqs can help.