Moving a website with MLS listings from WPL Pro is no from moving a regular Wordpress website.
The only  is that in most cases, a website with WPL MLS listings will be much larger in size.

First, before moving the website, please make sure the new server supports the requirements that your WPL website has.
You can find detailed specifications here:
https://support.realtyna.com/index.php?/Knowledgebase/Article/View/529

After moving the website, make sure, all the tables from the database are copied, compare them side by side and see if any tables are missing.
If you're not missing any tables, you should all good in the database.

After the move is done, you can now copy the jobs that were set for your website, they should be something similar to this:

17 0,12 * * * wget -O - 'http://website.com/?rets_cron_job=1&rets_cron_job_type=offline&time='$(date +\%s) > /dev/null 2>&1
*/5 * * * * wget -O - 'http://website.com/?rets_import_cron_job=1&time='$(date +\%s) > /dev/null 2>&1
0,30 * * * * wget -O - 'http://website.com/?rets_purge_cron_job=1&time='$(date +\%s) > /dev/null 2>&1

Please make sure you move all the  jobs and the exact time intervals that were on the previous server.
Also, if you've changed the website domain, make sure to update the  jobs with the new domain.
Once you've  should continue to function as it was before.