So many comments saying "Fire the guy" without any kind of investigation. And almost universal acceptance that what the woman said is the end of the fact-finding needed to make a decision.

In previous lives as a senior manager and litigation paralegal, I have had to deal with dozens of sexual harassment claims, including the kind that end up at the EEOC and a few that resulted in lawsuits. A good friend and former coworker is a regional HR manager for a Fortune 100 company, and he has seen everything under the sun.

OP, the only reason to do anything is because you're the founder and she brought it to you. You don't have to do anything other than document her conversation with you, but if you decide to stick your nose into it, here's what my thought process would be:

First, even if it's a small startup, OP cannot discuss with the accuser what action he takes with the accused beyond "I'll handle it." While this may baffle many here, it's really none of her business since it involves the accused's relationship with his employer. If he ends up firing the guy, she can put 2 and 2 together, but he cannot provide details of disciplinary action.

Second, he cannot announce to the rest of the employees that he fired the guy for sexual harassment, only something along the lines of "he no longer works here" with maybe some generic fluff about pursuing other opportunities. It's none of their business either.

Third, he needs to talk to the guy. "But she showed him the texts!" someone exclaims. "He called her a MILF!" That's one side of the story. Let's hear the other side before jumping to conclusions. This all happened outside the work context. We don't really know what the hell happened, only third-hand reporting of one of the participants.

Fourth, let the HR person talk to the lawyer, if OP's startup is big enough to have a dedicated HR person. If not, then yes, talk to a lawyer, but make sure they've got some litigation experience. Too many HR lawyers are just overpaid risk managers who don't have any clue of when to fight and when to fold and pay.

Which brings me to my last point: I know it may be unpopular to say, but sometimes women lie and manipulate just as well as men do.

At my senior manager job, I was accused several times of sexual harassment, even though I scrupulously avoided any kind of personal conversation that could lead to any hint of anything sexual with all coworkers, whether direct or indirect reports, peers, or superiors. I never met behind closed doors with women, except my boss, and she always left the blinds open and people felt free to interrupt at any time. And yet, I was accused. None of those accusations withstood scrutiny, but they were a gigantic PITA.

One crazy person even reported me to the FBI, after the EEOC found nothing actionable! (Seriously. The issue was that I was her last resort for altering an unfavorable survey given to her by a customer, and I refused to do so, for sound business reasons.)

Texts can be faked. We don't know enough to know whether the accuser's story is absolutely true and complete, and we certainly don't know her motives.

OP, find yourself someone with serious experience in employment law in your jurisdiction to give you counsel. Pay their fees. Stop trying to do it on the cheap by asking here, since it will do you no good and quite possibly do great harm to follow 90% or more of the advice in this thread.

Edit: added paragraph about doing nothing, and fixed "autocorrect."