Can 2 Different PS4's From Different Houses Use the Same Account?

I'm moving out soon, but I've been sharing the ps4 account with my older brother. The house I'm moving too has a ps4 too, but i'd like to use that account there too because I'm not taking my brother's ps4 with me and I'd like to use the same things like dlc i bought from the games I'm bringing with me. So can i log in that account into another ps4?