this sounds very bad OP, sorry, but it does. Im very much for fighting overly jealous feelings - having been driven mad by them in the past - BUT - you have to be able to trust your partner.
Please do not even think about messaging her - its your husband who is behaving deeply inappropriately here.
Funnily enough something similar happened to me - an old flame sent a text to my DP saying 'dreamt about you last night - what could that mean'...he IGNORED IT. he told me 'god, what a nutjob, why is she sending me inappropriate messages, Im embarrased for her.'
In the early days when I was paranoid, he said to me - you can look in my phone any time you want, I've got nothign to hide.
Im afraid you are looking in the wrong place - your H should not be messaging this woman and you know it. Ask politely to see his messages, saying you are feeling a bit upset about it all and would like to know what they talk about.
Do not be put off if he accuses you of being crazy - I promise you, a good man would be sad and sorry that he had upset you.
this is meant to be your husband - your best friend and person you trust most in the world. There should not be secrets and he should not be doing this.