What you want (WeatherLink JSON to Weather-Display clientraw.txt) is possible, but will be complicated.
The JSON data from WeatherLink.com appears to have the units you set to record data in your weather station.
The clientraw.txt file is always using units of C,kn/s,hPa,mm for temp,windspeed,pressure,rain so there would need to be the capability of units conversion for each data entity. Also, there are data in clientraw.txt that do not exist in the JSON (like text description, icon number, etc.) so some provision to provide them (or use a null entry) would have to be done.
Accessing the JSON with PHP is simple.. you use the function json_decode() which can place the results in an array or in a class structure (like you use when using the XML decode function).
I'd suggest you start with what the data definitions are for each field in clientraw.txt and in a spreadsheet, annotate which ones appear in the WeatherLink JSON as available for your use.
I did a similar thing for the WLCOM plugin to the Saratoga template set. You might take a look at that and see what's involved. It can create a 'realtime' file like the Cumulus realtime.txt file, so the same method could be done for a clientraw.txt file with a goodly amount of rewrite. WLCOM plugin at
https://saratoga-weather.org/wxtemplates/WLCOM-plugin.zipThe WD clientraw.txt field definitions can be seen at
https://saratoga-weather.org/wdparser.phpHope this helps...