Ukraine Foreign Assistance Integrity and Accountability Act of 2019 This bill requires various actions relating to sanctions generally, and against certain Russian entities specifically, and calls for investigations into the delay of assistance to Ukraine. The President shall immediately obligate funds appropriated for certain security and military financing assistance to Ukraine. The Department of State shall immediately produce for Congress records related to (1) military assistance to Ukraine, (2) requests to investigate any candidate for the 2020 U.S. presidential election, (3) the President's personal attorney, and (4) the President's July 25, 2019, call with the president of Ukraine. The State Department inspector general shall investigate and report to Congress on inappropriate interference into foreign assistance for Ukraine. The bill establishes within the State Department the Office of Sanctions Coordination to advise on the development of sanctions policy and to represent the United States internationally in sanctions matters. The President shall impose asset- and visa-blocking sanctions against persons and entities that (1) facilitate illicit and corrupt activities on behalf of Vladimir Putin, or (2) knowingly engage in significant transactions with Russian entities that facilitate malicious cyber activities. The State Department shall periodically certify to Congress whether Russia is interfering with freedom of navigation in violation of international law. If so, all Russian shipbuilding entities shall be subject to economic and trade sanctions. The State Department shall take various actions to implement and expand activities to counter Russia's malign influence in vulnerable countries.