check (one's) bags through (to) (some place)
To request that one's luggage be sent to one's final destination, as when traveling through multiple cities or via different modes of transportation. I don't have any luggage with me because I checked my bags through to Rome. Just check your bags through, and then you don't have to worry about keeping track of them at every stop.
check someone's bags through (to some place)
and check someone's luggage through (to some place)to have one's luggage sent directly to one's final destination. Please check these bags through London to Madrid.