From Longman Dictionary of Contemporary Englishbox numberˈbox ˌnumber noun [countable] TCMan address at the post office that people can have their letters etc sent to instead of their own address → PO Box
Examples from the Corpus
box number• Each one was labelled with a box number and contained a large brown envelope.• You have to get letter heads printed, make it look good, have a fake box number.• I never wrote to that box number.• I wrote that night to the box number.• So she wrote to the box number and suggested a date for a preliminary viewing to avoid disappointment or misunderstandings.From Longman Business Dictionarybox numberˈbox ˌnumber (also post office box number) [countable] an address used by a firm for receiving letters at a POST OFFICE instead of its own addressIt is usually best to avoid box numbers in advertisements as they tend to put people off replying. → number 