What would you do??!

Okay, this might be a bit long winded but I need to get it off my chest and hopefully get some insight if anybody else has been thru this. First, I’d like to start by saying my hubby is the most selfless, SHY, caring dude on planet earth. No joke. We’ve been together for a long time and not ONCE have I ever felt like he’s even thought about another woman. We are literally best friends and are always together. I always say we have the type of relationship other women dream of. Soo, please keep this in mind. A couple weeks ago, he had just gotten home from work and I left with my mom to the store. While we were at the store I got a call from him and he was bawling. If you’ve never experienced that sinking feeling in your stomach, where you even get a little tingly and light headed consider yourself lucky! A few things flashed before my eyes -family member was hurt or passed, something happened to one of my dogs, he was hurt ... but none of these were it. He just asked me to come home ASAP. He said “I’ve been placed on administrative leave from work” (he works for a cable company, so he goes in peoples homes and installs the equipment.) Now, I know he takes pride in his work, so I could understand why this was upsetting, but the way he was acting you’d think it was catastrophic. As soon as I got home, he told me the whole story. HR contacted him and told him a customer (woman) had made a complaint against him, claimed “physical contact” had been made and law enforcement was involved. He just kept repeating “I didn’t do anything” and if I’m being completely honest - I wasn’t 100% sure if I believed it. And I always told myself I wouldn’t be one of those women that tolerates cheating, but I just told myself that I knew him and just didn’t believe it. We waited 3 excruciating days where we didn’t know what was going on -during this time he assured me many times that he would never do anything to hurt me and that he was going to prove it. He was proactive and contacted HR himself to find out what was going on, they gave him the name of the detective who had called in the complaint, when he talked to him, the detective told him he’d been busy and just hadn’t had a chance to call him, so my husband volunteered to come to him and he did. He was asked to take a lie detector test and my husband was more than willing, and guess what .. he passed. (I know these aren’t super reliable since they aren’t admissible in court, but the detective himself told him he didn’t have any reason to believe he was lying) Well, the very next day my husband was cleared to go back to work ... Now, here’s the thing. This woman made false allegations about my husband, it affected him tremendously because he’s such a respectful guy and just couldn’t understand why anybody would say those things. The exact complaint was that he had grabbed her breasts from behind and said “nice titties, give me pussy” My husband would not even be able to say this to me without giggling, so I am 100% sure that this did not happen. There’s also the fact that the complaint wasn’t made until TWO WEEKS AFTER he had gone to that house. He said the lady was older, and other than being grumpy didn’t seem out of the ordinary. So WHY would she do this?? I just can’t understand. At this point we are both just angry. Especially me, being a woman, I don’t victim blame, but this lady was NOT a victim, she’s just psychotic. I want to sue her personally for defamation of his character, but my husband doesn’t want it affecting his job. He thinks his job was supportive because once he was cleared, his manager and coworkers assured him they didn’t believe it for a second and they would’ve advised him to go after the company AND the customer if he’d gotten fired, plus they paid him for the time he was off. So, I’m wondering if anybody has any sort of advice ? Should we pursue a lawsuit or just move on?