I would assume that the other databases are Postgres as well? And all of them have only one schema? If you only have to do it once, then the easiest way is to use pg_dump -Fc
to export the database and then edit the resulting SQL file by some regexp script.
In detail, you will have a
SET search_path = public;
row near the top of the file. Rewrite 'public' to the desired schema name. Other places to check for are where a stored procedure returns a user-defined type, view or table rowtype, here you will see something similar to
CREATE OR REPLACE FUNCTION f()
RETURNS public.my_view AS
...
Rewrite 'public' in such places as well.