This is where an exfil (exfiltration) route is needed. You could just send the data to a server you own, but you have to make sure that there are fallbacks once that one gets taken down. You also need to ensure that your exfiltration won't be noticed by a firewall and blocked.
Hosting a server locally, easily, on the infected PC, that can expose data under a specific address is (to my understanding) the holy grail of exfiltration; you just connect to it and it gives you the data, instead of having to worry much about hosting your own infrastructure.