I have a Shopify store as well as Amazon. I have my higher velocity products set up as FBA and my lower velocity as FBM. I offer free shipping and free returns, so I provide the return label to customers.
My question is around process returns for products sold on Amazon, but fulfilled by Merchant. Right now, I am creating a return label in shopify and then uploading the return label image through Amazon Seller Central. I have not tried using Shopify to send the return label to the customer. Before I try doing that for my next return, I thought I would ask the community if that works, or if there are any problems (since Amazon is somewhat limited in what they allow for communication with the customer).
As long as your communication is to help give the customer good service, and isn't directing them with links to your website, I think it's ok to send your own return labels (you can contact Amazon support to make sure 100%).
We use an app called Shippo to do this in a store I'm involved in. It's easy and keeps all our shipping costs in the same area.
For FBA products we do the same thing, so we can inspect the returns rather than having them go back in the bin at Amazon.