$*, unquoted, expands to two words. You need to quote it so that someApp receives a single argument.
someApp "$*"
It’s possible that you want to use $@ instead, so that someApp would receive two arguments if you were to call b.sh as
b.sh 'My first' 'My second'
With someApp "$*", someApp would receive a single argument My first My second. With someApp "$@", someApp would receive two arguments, My first and My second.