Stop Illegal Trafficking in Firearms Act of 2017 This bill amends the federal criminal code to establish stand-alone criminal offenses for trafficking in firearms and straw purchasing of firearms. The bill expands the categories of prohibited persons (i.e., persons barred from receiving or possessing a firearm or ammunition) to include persons who intend: (1) to sell or transfer a firearm or ammunition to a prohibited person; (2) to sell or transfer a firearm to further a crime of violence, a federal crime of terrorism, or a drug trafficking offense; or (3) to unlawfully export. It increases the maximum prison term for the sale or transfer of a firearm to or the receipt or possession of a firearm by a prohibited person. The bill revises existing prohibitions on: (1) transferring a firearm knowing that it will be used to commit a crime of violence or drug trafficking offense; and (2) smuggling a firearm into the United States with the intent to unlawfully import or to promote a crime of violence or drug trafficking offense. It broadens the scope of and increases the maximum prison term for violating the prohibitions. The bill also makes it a crime to smuggle a firearm or ammunition out of the United States, or to conspire or attempt to do so, with the intent to unlawfully export or to promote a crime of violence, a federal crime of terrorism, or a drug trafficking offense. Finally, the bill prohibits the Department of Justice, or its law enforcement coordinate agencies, from facilitating the transfer of an operable firearm to a known or suspected agent of drug cartel, unless U.S. law enforcement personnel continuously monitor or control the firearm.