My brother is who, long ago as kids, got me into wargames and strategy games more generally. 20 years of marriage and family has hampered our ability to play with and against each other, and he kind of flatly refuses to get a PC for that purpose (nor to convert the family PC for that purpose. He has his reasons, mostly wifely.

)
Consequently, while he has Android tablets and phone on which he COULD play games, and occasionally DOES, we don't have a clear idea what strategy games can be played cross-platform.
The triumphant adaptation of
TWILIGHT STRUGGLE is of course a cross-platform game that he could play with me on my PC. ...I think. I'm not totally sure if the Android version is cross-platform mp or not. If it's cross-plat between those platforms however, then aside from the question of whether he would appreciate the topic it tics important qualifier boxes:
1.) turn-based not real-time;
2.) the turns must be asynch, because neither of us knows for sure when the other will be able to play;
3.) not chess (he doesn't care for chess

).
Real-world strategy since the industrial revolution would be very much a plus. Combat strategy would be very much a plus. (Non-combat strategy would be easier in family politics, so to speak

, but I don't think he'd care for a game of Carcassone or Le Havre or Agricola or Stone Age etc.)