I use PushBullet in the Google Play Store. You install PushBullet on all of your devices (even Windows and Mac computers, Android Phones, IOS and they also have browser plug-ins for every browser out there.
Once installed on each device, you have to sign in with your Google credentials.
Now, when a text (or any other notification comes in such as a Facebook message or what have you), the app gives a pop-up on the computer or tablet allowing you to respond to the message, dismiss the message, mute the app, etc.
It doesn't sync your text message history onto each device, but it does allow you to receive messages on each device and respond to them. Your cell phone, of course, has to be powered on, as the messages are still being sent and received via your phone and relayed to your other devices.
If you are running a device any earlier than Android 4.4, you can't reply to messages, only receive them.
Another feature of PushBullet is that you can send files, links, photos, etc. from your PC to your device, and vice versa. It's an easy way to transfer files.
Their website is www.pushbullet.com