Haven't played it or used the save-set, so take my advice with a grain of salt: When you say you beat the Moonlighting mission, was that on your own save (meaning, before you resigned and copied this one over), or was that on this save from Blurrz? Either way, if you're having any trouble at all with a save not doing what you think it should, then I would delete all the Mafia DE saves from your PS4 (back them up first somewhere of course), then copy over this resigned save only after you are sure that there are no Mafia DE saves on your console. When you boot the game up, make sure your console is offline (probably doesn't make a difference in this game but you'd be surprised sometimes). This is all to make sure there are no save/data conflicts. (Also make sure to choose "load" so you manually pick your save, instead of "continue" which lets the game automatically choose a save, but there is only one save in the Made Man folder so that shouldn't be an issue if you've deleted all saves. And I'm not sure if Mafia 1 even has a "continue option anyway.)
I should probably also point out that this likely isn't the right forum for your question. You could also try posting your question right to Blurrz's thread. Either way I hope you get this resolved soon.