Stop Illegal Trafficking in Firearms Act of 2019 This bill establishes stand-alone criminal offenses for trafficking in firearms and straw purchasing of firearms. It 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. It broadens the scope of and increases the maximum prison term for violating 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 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, it generally prohibits the Department of Justice and its related agencies from facilitating the transfer of an operable firearm to agents of drug cartels.