Polygon editor is much faster when you want a hard paint. Weight Brush is necessary to ensure actual bending is appropriate.
Right-click in the viewport with the editor up and choose selection mode-rectangular select. This mode selects all the way through the model, so make SURE you are in front view.
Drag a square around the sleeve area that you want to reassign. It will select all the target verts. Reassign them in the Polygon Group Editor, but don’t deselect yet. Instead, switch to Weight Map Brush. Don’t worry, you won’t actually have to brush anything! Select the forearm bone in the scene tab, then go look at the WMB tool settings.
You should see things that say X Axis with Xrotation under it, and the same with Y and Z. For this item you can probably ignore the Bulges (xbulge, ybulge etc).
Now, if you have the polygons still selected, you can click on Xrotation and see how much or little they are painted to the area you want. Right-click in the viewport and choose Fill Selected Faces and 100%. Now you have red. Repeat for Y and Z.
Optionally: For smoother deformation, while you have a group selected, choose Smooth Selected Faces and choose around 1/3 of the slider length and 40%. If this doesn’t provide a “hard” enough paint, undo and leave it at 100% at all the edges and just leave smoothing on.