I use Google Voice for my phone, for voicemail and SMS. It is very convenient to read and send texts from my computer, but if I do not use the Google Voice app on my phone (which, unfortunately, is rather ill-designed in my opinion), the texts I send from voice.google.com or the Chrome extension (or, incidentally, the Google Voice app on my phone) do not show up in my SMS thread, in the stock messaging app or any replacement one (I use GoSMS).
Is there a way to make Google Voice sync with these somehow, so I can see the messages I send through Google Voice without using one of their apps?