At the family manager account Fortnite Save the World bought. Can other users play this as well?

We bought a Fortnite Bundle from the Family Manager Account and my son can't play it. He has his own account and no access to the manager's account. How can I allow him access to the bundle?

Because they have the Family Manager Account, they need to connect their son's account. Depending on which console their son is playing, they have to manage this in the settings on their website. After that is done, they can give their son the Save the World mode / grant permission.

We both play on Ps4. Can I then connect the accounts directly? If yes how?

Exactly, you can connect the two accounts directly on the official Playstation page, which is possible in the settings, the family account.