My understanding (and I could be wrong, I haven't tested in a while) is that if you send a host or co-host to a breakout room, they should be able to share their screen and present content.
If it's an attendee you want to be able to share their screen in a breakout room, you need to make sure they're allowed to do so first in the main room. Check under the Security button in the meeting controls to see if you have "Participants can Share Screen" checked.
The safest and easiest way is to schedule the meeting with the folks you want to present in breakouts as alternate hosts, or make them co-hosts when the meeting starts. This way you don't have to worry about someone who isn't supposed to share content starting to share their screen and putting up inappropriate content.
Also, definitely test this ahead of time. Set up a practice meeting or two to make sure everyone you need to present can present.
Good Luck!