A president DOES NOT have to be clear on which act is being pardoned.
This is from NIXON's pardon:
Now, THEREFORE, I, GERALD R. FORD, President of the United States, pursuant to the pardon power conferred upon me by Article II, Section 2, of the Constitution, have granted and by these presents do grant a full, free, and absolute pardon unto Richard Nixon for all offenses against the United States which he, Richard Nixon, has committed or may have committed or taken part in during the period from January 20, 1969 through August 9, 1974.
All HUSSEIN had to do was change the name and the dates. He could go from the beginning of the republic up to and including the minute that President Trump was sworn in as president. In reality, he probably signed pardons in the days/weeks leading up to the change in president.