I've done the 3 speed conversion with the DT swiss shifter on a 2019 Brompton. I wanted more range on the gearing, not just 3 gears, I went to 12 - 15 - 19t.
I just found shimano sprockets which looked right and tried them. I didn't know what I was doing really and could find any info on it. I believe 17t is the spec limit but several people said you can go to 19t with barely any frame rub, possibly 21t if you're prepared to file a mm or two off the frame. I wasn't.
The only surprises were that I needed a thinner circlip and a spacer for the chain tensioner to stop it rubbing.
The shifting is pretty good actually. I got the DT swiss shifter expecting I may have to switch to friction, but it's fine. Just get an inline chain tensioner.
Weirdly the drivetrain is noisy in the mid and high gears. I thought initially it was poor chain alignment, but they should be better aligned than the low gear? Maybe I have the wrong chain length? Maybe the chain tensioner is compromised for this gear range?
There's a thread on this that no one uses BTW: https://www.lfgss.com/conversations/228623/
Sprockets I used:
12t: Shimano CS-5800 Sprocket 12T for 11-28T/11-32T with Built-In Spacer (Design 12T)
I guess I reused the 15 or 16t one that came with the Brompton.