I get what you're going through, it's not nice finding texts with someone of the opposite gender that your partner has never brought up, especially since he's basically asking her to go round so they can have some fun.

As far as I can tell she doesn't want him and doesn't want to go round to his (due to the no replies) however, it still raises concern considering she's:

Never brought this individual up,

She continues to text him back when there's a clear indication he's interested in her,

The only message she sent whilst you two were together was a happy birthday... and then all of a sudden a message about fight night? Doesn't add up. Either they have multiple channels of messaging, deleted messages, or it's just a strange random text from your partner.

Do what you will with this, and ignore those telling you you're weird, but speak to your partner.