To make it truly interesting you'd have to add a geostationary relay satellite and e.g. solar recharging, to make the device useful for up to a lifetime. At this point, we have a military communications device of obvious value. (Presuming you get to a non-idiot.)
British GDP was about $10.7bn in 1700 in 1960 dollars PPP [1] or about $113bn today [2]. At its height, in the 16th century, Britain spent about 10% of its GDP on its military [2]. So our price for a working pair of satellite phones is reasonably capped around $11bn in today's money. Of course, having a pair of satellite phones and no military isn't helpful, so in practice we'd likely see a top price equal to about $1 to 2bn today.
At which point one asks what size army one could raise to steal your satellite phones with a fraction of that money.
[1] https://en.wikipedia.org/wiki/List_of_regions_by_past_GDP_(P...
[2] https://www.usinflationcalculator.com
[2] https://eh.net/encyclopedia/military-spending-patterns-in-hi...
That would indeed be something.-
Had originally limited battery to a week in the thought experiment as I was curious about what would happen after they became mere "inert" objects.-
(Image the Pope being summoned - and a church Council being called for and the device suddenly ceasing to work - with hundreds claiming it once did ...)
That would be quite the "footnote" somewhere ...
PS. I hate to "underestimate" our forebears, but ... at what point would they just throw their hands up in the air and start screaming "witchcraft!" burning the lot, phone samples and all, at the stake?