Protect Election Integrity Act of 2020 This bill requires states to establish certain election measures. It also prohibits ballot harvesting in federal elections. Specifically, the bill requires each state, in order to receive certain election assistance funds, to prohibit the knowing collection and transmission of a ballot that was mailed to another person (commonly referred to as ballot harvesting), with exceptions; permit poll watching by at least two appointed campaign representatives per campaign; require absentee and mail-in ballots to be counted and recorded immediately upon receipt without disclosing any results until after the closure of polling places on election day; require continuous counting of ballots after the closure of polling places on election day; install video surveillance of ballot drop boxes; require each supervisor of elections to make publicly available a report outlining preparations for the upcoming general election; and require an audit of municipal voting systems. Finally, the bill generally prohibits ballot harvesting in federal elections, which is the process of collecting vote-by-mail ballots from voters and returning them to the polling place or election office. A violator is subject to criminal penalties—a fine, a prison term of up to five years, or both.