It sounds as if you are not using Vault. What version of Inventor are you using?
Is this what you mean by shared project?

If so, I strongly recommend that you not use that option. It only exists to support ancient workflows from before Vault existed, and you can't use it unless you specifically enable the ability in Application Options.
Autodesk Vault is exactly what you should be using if you need to share project work amongst more than one or two other users. Vault Basic is included with your Inventor license; Vault Professional is extra cost. There is some significant time investment required to get Vault set up and working for you, but it then manages sharing for you, as well as providing other useful tools (more with the Pro version, of course).
However, if you only have a few users, co-located, it isn't all that difficult to manage sharing by the really old-fashioned method of just talking to each other... !
For your current issue, you'll have to open the assembly in question and figure out how to check it in so it's available to other users. We briefly tried using a Shared-type project at my last workplace about twenty years ago, but I've long since forgotten how to work with it.
Sam B
Inventor Pro 2025.0.1 | Windows 11 Home 23H2
