Well, why would you use an F23 tranny when the entire transmission/engine swap is relatively cheap? The H22A4's transmission offers shorter gearing to allow for quicker acceleration. If you plan to do this, may as well do it right.

The F23 transmission bolts onto the H22A just fine, and given they fit, I imagine the clutch couldn't be that much smaller on the F23, so it probably won't have problems handling the power.

But like I said, why bother?