Transferring DTV Streaming box to another smart tv in another state?

We have DTV Streaming service over fiber optic cable in north Florida.  (Correct terminology?)  We purchased our DTV streaming box from DTV.   We will be spending time in Maine where the only cable and internet service is through Spectrum, which has a monopoly in our part of the state (ugh).  We were told that we could just unplug the streaming box here in Florida and plug it into our smart tv in Maine and discontinue Spectrum's cable service, just keeping wi-fi.  Does that make sense?  We are not tech savvy, and my husband is reticent to change anything that's [usually] working.  But I would love to decrease reliance on Spectrum in any way possible.  TIA.