@ScottRempel@Navigando@svikins
Here is the thing, disc wise it can work of course. You can install the game on any device as much as possible using the same discs, there is no problem there.
However, the problem begins with the game code itself. To play a game, you need to have it registered on your account (in this case your brothers account) and to do that you need a special one time use only code that is given in every game box that comes with the game (you used one of this to be able to play the game yourself already).
Since you used the code on your account to activate the game, that code is now tied to your account and your account only and can not be transferred to another account. Your brother could force install the game but when it then comes to playing it, the game will ask him for the activation code in order for him to actually access it and play it and if he tries to use your code he will get an error that it has been already used up. So unless your brother has an active version of BF on his account already, he will not be able to play it sadly. The only way would be for you to give him access to your account and that is not recommended for obvious reasons. The other way would be for him to buy an unused game code from a retailer or the PS store and then he can install it from your discs and play it as much as he wants but he would still have to get the game himself etc.
As for people selling used copies of BF online which you may have saw, that is illegal and not allowed and if they are caught they are banned by the TOS team. Plus if they are just selling discs, those wont even work without a activation code so that is basically fraud as well unless they are selling torrent versions which is also illegal too and will 100% not work.
So in basics, can he install the game from your discs in his device? Yes, he can. But can he play the game after without an unused activation code or an active copy on his account. No, he cant, sorry.