Sandgrounder ... most phones / networks (if not all of them) also understand the + thingy.

All numbers in my phone are programmed like this (obviously without the leading zero for European area codes)

+41xxxxxxxx for CH numbers
+49xxxxxxxxxx for D numbers
+1xxxxxxxxxx for US / CAN numbers
etc.

Usually SMS'es from anywhere to anywhere work fine nowadays. Used to be different 5 years ago when you couldn't even send a TXT from one U.S. carrier to the next.