According to books such as "¡Es la microbiota, idiota!" (ISBN 8413440688 but I don't know if it's available in english) it's not that simple, I think they said that not all the strains are identified and even then there are strains that aren't easy to grow in vitro (I'm NOT a scientist, don't quote me on this, I just listened to the audiobook).

What they make a point on is diet, she insists on the importance of having a diet that gives desirable bacteria strains an environment where they can thrive to achieve a balance.

IIRC she also mentions how it's not as simple as having "good" and "bad" strains and how balance is key.

It's a really interesting and funny book to listen to if you have a few hours for it.

So in the case of OP I think you're right about finding out more about the donors diet and replicating it as well as adjusting anything necessary for the newly arrived colonies to last through time.

I don't know sh!t about it nor do I intend to sound like I do so please correct me if I'm wrong.