With websites infected with malware, viruses and malicious content we usually transfer them to aquarantined area on one of our servers, clean the files and database, restore core files, and then transfer them back to the source. More often than not they are transferred to a more suitable host or to one of our secure servers.
This consisted of updating the Joomla version, along with the template and all extensions, implementing additional site security measures, along with automated daily site backups.
Excellent work. High degree of commitment and expertise. Nicely done!