Se você quiser combinar o texto na ordem, tente:
$ grep 'The.*password.*of.*user.*will.*expire.*within.*the' file
foo#foo_ehh113#The password of user 111 will expire within the next seven d
foo#foo_ehh204#The password of user 111 will expire within the next seven d
foo#foo_ehh204#The password of user 222 will expire within the next seven da
foo#foo_ehh113#The password of user 222 will expire within the next seven da
foo#foo_ehh113#The password of user 333 will expire within the next seven day
foo#foo_ehh204#The password of user 333 will expire within the next seven day
Se você tiver um arquivo para armazenar o grupo de texto, chamado group.txt, você pode usar:
$ grep $(printf "%s.*" $(cat group.txt)) file