So, the structure of phrasal verbs here is "fax+through+to", isn't it? Is it right to say "Could you fax this to the head office" directly? Thanks in advance

to fax through is a phrasal verb, you have to add through after the verb to fax ! phrasal verbs are usually a two-word phrases consisting of verb + adverb or verb + preposition. They are very numerous, considerably used in english language and quite useful as well. You can find lists of them on the internet.