Display specific galleries across multisite sub-sites


I have a photography site. Some of our clients want us to host their websites so galleries specific to them are displayed as soon as they are uploaded to our website. Using multisite to build the clients websites has been recommended to me but we're struggling to work out how to display client specific galleries on the relevant sub-site.

Ie: We take photos for client #1, #2 and #3. We upload them to individual albums on our primary site, the albums of which are displayed together. We then want only client #1's album to be displayed on client #1's sub-site, only client #2's album to display on client #2's site and same with client #3.

We want to automate the process of uploading the content to each sub-site and eliminate the need to create an album on every sub-site using network shared content.

Does this sort of feature already exist, perhaps by way of a plugin that uses tags to identify which galleries you want to display? Or is there something else someone can recommend to me?