The 90-91 B series trannies have different spline counts then the 92+ as I previously mentioned. It doesn't matter if its a LS or B16, I ran into this issue once when I went form a cable B16 (smalll spline) to a cable LS (large spline). Thats why I asked the OP what year his trans and car was. If he has a 90 Integra then he has a small spline clutch, but if his trans is from a 92-93 JDM XSI then he will need to change the clutch to the bigger spline style clutch. Again thats why I said before saying "oh yeah it'll bolt right up, questions needed to be asked".
You are correct in saying they will bolt up to the motor, however its the clutch that becomes the issue here. To the OP, just try putting your input shaft inside the clutch before bolting everything up to make sure it fits. If it does then you're good to go, if it doesn't then you now know you need a different clutch.
What code is on the side of your transmission (the b16 one), that right there will tell you what clutch you need to use. If it says YS1 then its a 92-93 XSi trans.
If its stamped with either J1/S1, then its from a 90-91 DA6 (XSI)