Since you don't have the full details you don't really know what the truth could be in the whole story. The fact that he doesn't reach out speaks volumes. Some people are really okay not having family members in their life. You need to let it be.

My only thought is stay out of it.

It is certainly not beyond the bounds of possibility that this toxic prior failed family progeny was so toxic that cutting her out of his life was self preservation for this man.

A 14yo is long past old enough to know right from wrong and to realize the results of their choices.  

I would be far from likely to let a kid of mine go, but, neither would I tolerate toxic teen bullshit.

I think we know all too well that stepmoms (the GF in this case) get the blame for many things that are not their fault. So I wouldn't automatically believe this story to be true. It might be. But it might not be.

I think if DH wants to try to have a relationship with the older SD, he should try to have one. The occasional text ("thinking about you, hope you are well kind of thing") is fine. Then if she responds, take it slowly.

But I don't think it's really your business, other than supporting DH if he wants to contact her, or if he doesn't.

You really need to stay out of this, if and when your DH is ready to contact the daughter, let him take the steps to do so. As other poster said you don't have the whole story of what caused the separation. For all you know the SD can be Hell on Wheels and if she comes back into your DH's life, she could make your life living hell. A lot of father's that have been in this type of situation and reunite with the adult skid are Disney Dads and you will find yourself in second place with the SD being your DH's priority. 

The fact that DH and SD have not connected after the girlfriend left says a lot. I would leave it be. If they reconnect they will on their own.

I'm sure that he does miss her. I might suggest that he give her a call but I wouldn't push it, you really don't know what kind of Pandora's box you will be opening.

Do you know what the original fight/fall out was about? Do you know anything about this girl? Like is she a problem child, or why the GF didn't want her around? I don't find it hard, at all, to believe that the GF had something to do with him losing touch with his daughter, it happens all the time. Not all step mothers/girlfriends are good, non-selfish people, who are accepting of the partner's relationship with his kids.

Once a certain amount of time went by with no contact, I'm sure he felt awkward about reaching out, so just didn't do it. That is not uncommon, especailly with men. I'm sure his daughter feels completely rejected, so she does not want to reach out to him, either.

I know you want to help him with this void in his life but tread lightly.

To be honest, and I've been there, the best decsion is the one he makes himself. So, if you suggest he call or text her and he doesn't, let it go. You can be supportive but don't push it.

If he was willing, back then, to go to therapy with his daughter, he should have done it. If he really did let his GF discourage him, he has some amends to make.

I do not like my oldest SD but I have never told my DH he couldn't have a relationship with her. I stayed out of it, and she imploded it all by herself.

My DH is estranged from his 3 oldest and only has contact with YSD 20.  He was attacked and had his shoulder broke. It took some time and therapy but there comes a point when the skids are adults that it falls to them to make an effort too.  Until you learn just how bad it was, you need to respect his decision.  This could be a nasty Pandora's box if opened.  Only he will know that.  He still has contact with the younger one and that's good. Some journeys aren't for us to travel. This is your DH's path to walk.  If he wants to reach out you might suggest some short term therapy for him to get guidance on this. Someone experienced with children of divorce and the issues they can have.  

My SO mourns the loss of OSD any parent would. It does not mean they should put forth the effort to reconnect and open old wounds they have worked to heal.

SO doesn't want to engage with OSD at this time because he can't handle the drama she brings with her. She is BMs flying monkey, her golden child. She makes every effort to engage in behavior meant to punish SO. Whether that be verbally abusing SO, belittling him. Trying to cause conflict between SO and I with lies and deceit. Winding up YSD by gaslighting her into believing she is being treated unfairly. That is his choice not mine. 

SOs sadness is in losing the little girl who loved him and enjoyed spending time with him. She was his pride and joy, his buddy. They did everything together and now she acts as if she cannot even stand the sight of him or the sound of his voice.

She can use whatever excuse she wants for her behavior, choices and actions. Blaming me, blaming him. At the end of the day the only one who controls her behavior and actions is her.

Does he hold on to hope that girl may come back. Of course. But as time passes that becomes a fading thought. 

Why do you call it --dh's abandoning his kids? Did he also stop paying child support AND/or stop health insurance IF he was covering them?

Kids don't reject a parent in this way. Kids DO get mad and stomp off, huff and puff to their rooms OR to a friends house...then they slowly start to reintegrate back to the clan.  have you ever noticed that with your own kids IF you have any? IF not, watch the next time they get mad at you for something.

Assuming your dh didn't sexually abuse his kids over a long period of time. There is more to the rejection than just a gf problem from the past..

Behind every kid who rejects their non custodial parent,  there a bm lurking behind the curtain.