The catalog that you are sharing should have information_schema.table_tags and information_schema.column_tags tables . You can share these two tables as well if you are not sharing it today . 

You can then ask your share recipient to join these tables to the tables you have shared to get details on the tags for each table and column . You can also get creative with using the tags from table_tags and column_tags to define your comments value when creating share and see if that help propogate the tags.