How do I save (send to email) an old conversation I had on my Samsung Galaxy s2, after verifying whatsapp on my new phone already?

I bought a new phone (oneplus one) and I already verified my new whatsapp account on that phone. Can I still get back my old conversations that are on my Samsung galaxy s2? I need one specific conversation that I had on my old phone. I want to send that conversation to my email. However, when I go to my old phone, I can not watch my conversations in there. I need to verify it first.

How do I save (send to email) an old conversation I had on my Samsung Galaxy s2, after verifying whatsapp on my new phone already? I never deleted my old whatsapp conversations on my Galaxy s2, but never back-up'd it either.. Everything is still on my S2 (I hope).

Thnx a lot!

Is it a problem when I never back-up'd? Do I need to get in my whatsapp on my old phone first (and verify that one to get in my old messages on that old phone) and back-up from there first? I didn't back-up my whatsapp on old phone before verifying whatsapp on the new phone that I use now. However, I didn't delete any data of old phone either..

To make it understandable:
1) I didn't back up my whatsapp on old phone (S2).
2) I bought a new phone and opened and verified whatsapp.
3) Now I need a conversation that I had on that old phone (S2).
4) How do I get that conversation (as any readable file) to my computer?
5) (when I try to open whatsapp in old phone (S2) Whatsapp asks for a verification)
6) Do I first need to verify on my old phone (S2) to create a backup there? Or is that possible anyway?

Sorry for the complexity of all this.. But conversation means the world to me at this point. Thnx in advance.

No I didn't uninstall my whatsapp on my old phone. I just didn't back up. I know that in the beginning (after verifying whatsapp on my new phone) I could still see all my conversations at my old phone. But later when I checked it, it asked for a verification.