Often one might have to copy datafiles from one database instance to another (And hence one ASM instance to another), for eg: when copying datafiles from prod to development.
You can use the cp command in asmcmd to accomplish this. cp can copy files from one instance to another. You can specify the username/password@connecstring for the target asm instance in the cp command.
ASMCMD [+] > cp +data/orcl/datafile/EXAMPLE.265.691577295 sys/password@myserver.+ASM:/scratch/backup/myexamples.bak