GribinIsaf I don't know the answer to your question but you my have answered it yourself.
If you are willing to have a go (assuming your inverter is wifi-connected), you could set up your phone as a hotspot and allow the inverter dongle to connect to it and therefore the internet (over your phone 4G, if you have it). The simplest way to do this would be to give your phone hotspot the same name (SSID) as your home wifi (Settings-General-About on iPhone) and the same password (you may have to temporarily switch off the home wifi if there's a channel conflict and depending on your phone, it may offer a hotspot on both 2.4GHz and GHz bandwidths, or just one but the dongle will need 2.4GHz). You can force an iPhone to offer 2.4GHz hotspot by enabling "Maximize Compatibility" in the hotspot settings.
I'm not sure how much of your data allowance the inverter would consume, but you could give it a go if you're willing to try?
Let me know if yours is a wired inverter (ie ethernet) and I'll have a ponder how you could do that.