[n1try]

I'd be interested in that project, can you show it?

[gravypod]

I haven't made it. I've just started thinking about what I'd need to get it done. I'm a systems dev not an Android app person.

I want to make a thing that will forward my SMSs to a webpage so I can read them online and I want to be able to start conversation, reply to conversations, etc. I want it to be open source and free.

I'm not really interested in making it, I just want it.

[lighthazard]

IFTTT can do this for you without programming work. Requires your phone because texting requires money.

[swatthatfly]

look at Pushbullet, as a browser extension.

[gravypod]

This is not self hosted, open source, nor free.