[GENERAL] Extract from text id other table - PG 9.1

I've got tableA with 3 columns.

id(seriaL) | type(character varying(256)) | string(character varying(256))

I have the type/string value stored in another table, and from that i would like to get the id.

Example: http://dbfiddle.uk/?rdbms=postgres_9.6&fiddle=15c571caa36876f00a0a2eaace703a2b

How can I extract, from that tablea.type_m column the tableb.id value?

Thanks

Patrick