Two ways to go about this, depending on the type of policy you use.
Assuming your user is going to share access to a single item, you could add a resource policy to the item, in the S3 bucket. The resource policy would allow someone with the specific cognito Id to read that item. This is not as invasive as modifying the assumed policy of a federated identity.
The alternative approach is to change the role of the user you give access (share with). This is modifying the assumed role of that federated identity. You would have a condition that they can access theirs, and another users specific s3:prefix. I think this way becomes very complex, very quickly.
So with the first option you could have a share API call, that says, if the user who invoked this API endpoint is the owner of this item, then allow them to set that items resource policy, to also allow reads from a cognito identity with a specific uuid.
You can make use of conditions for the resource policy I believe:
https://docs.aws.amazon.com/IAM/latest/UserGuide/reference_policies_elements_condition_operators.html#Conditions_String