With the latest desktop versions, it’s no longer necessary to install Anywhere on your Republic phone first or at all. Anywhere will sync the last 30 days of text messaging history to your computer.
If not planning on replacing your phone and you wish to hang on to the number, you may want to think about parking it. NumberBarn is a reasonably priced choice: https://www.numberbarn.com. It’s a more complex solution but you might look at Anveo as well: http://anveo.com. Of course, there’s the option of moving your Republic number to another cellular service provider also.
If you do move your number from Republic, Anywhere would no longer be a solution for communicating via text message.