BrowserTexting Lets You Connect and Send Text Messages Through Your Android Phone
Android/Web: BrowserTexting is a combination Android app and webapp that allows you to send and receive SMS messages through your phone in your Web browser. This way if you're busy working, you don't have to stop and pick up your phone to see or respond to texts, you can do it in browser tab.
In order to use BrowserTexting, you'll need the app installed on your Android phone. Then scan the QR code that the service provides you to pair your phone with that browser, and text away, at least until you close the browser. If you install the service's Chrome extension, you won't have to keep pairing your phone, and you'll get pop-up alerts on your desktop when someone messages you. You can click the alerts to instantly respond, and manage your messages through a toolbar icon.
BrowserTesting is in beta, so keep that in mind when trying it out. Regardless, it worked well and could be a good way to send and receive text messages on your PC so you can leave your phone docked and charging during the day.