If it's a one-off you could take a backup from one server and restore it on the other server then copy the data with an INSERT INTO... SELECT * FROM...

It's helpful to read if you add a few new-lines to your code.
To add another inner join you could put it in like this:
select g.name,pu_id,ye_id,genre...

You need to have the agent job on the instance (Server B) which has the linked server connection to Server A.
Your queries will then be something like:
[code...

I've just created a function that will sort a csv column alphabetically:
CREATE FUNCTION dbo.SortAlphabetic
(
    @Text nvarchar(4000),
    @Delimiter nvarchar(10) = ';'
)
RETURNS...

You can use SQL Server 2016's STRING_SPLIT function to split the column by semi-colon into multiple rows.
You can then put the string back together in alphabetic...

If you create the stored procedure with a default value for @state of NULL, then if the parameter is NULL you can display some help for the call, e.g.: