How do I convert an integer to string as part of a PostgreSQL query?

Because the number can be up to 15 digits, you'll need to cast to an 64 bit (8-byte) integer. Try this:

SELECT * FROM table
WHERE myint = mytext::int8

The :: cast operator is historical but convenient. Postgres also conforms to the SQL standard syntax

myint = cast ( mytext as int8)

If you have literal text you want to compare with an int, cast the int to text:

SELECT * FROM table
WHERE myint::varchar(255) = mytext

You can cast an integer to a string in this way

intval::text

and so in your case

SELECT * FROM table WHERE <some integer>::text = 'string of numbers'