Hi,
If the sleeve is what came out, first, it can't be reused. It must be replaced. Second, there should be a snap ring on the stub shaft (part in the transmission that the axle splines into) that has come off.
Do me a favor. I attached the directions for the removal of the sleeve. Take a look through them. The directions mention the snap ring. Either it fell off or you are trying to install the sleeve over it which is preventing it from fully seating.
Let me know. Note: These are the removal directions. Installation is the opposite. There is a special tool that is used to fully install it. It is GM tool number J-41228. You may find a parts store that can lend one to you, but they really aren't too common. The directions mention a specific puller. Since it is already loose, that shouldn't be needed.
Let me know.
Joe
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Sunday, June 26th, 2022 AT 9:36 PM