Most scholars believe that the Constitution allows Congress to impeach former officials, including former presidents, but Stanford law professor Michael McConnell points out that isn’t the question facing the Senate today. McConnell writes to Eugene Volokh at Reason:
Whether a former officer can be impeached is beside the point. Donald Trump was President of the United States at the time he was impeached by the House of Representatives. The impeachment was therefore unquestionably permissible (putting aside any disagreements over the nature of the charges).
Article I, Section 3, Clause 6, states: “The Senate shall have the sole Power to try all Impeachments.” The key word is “all.” This clause contains no reservation or limitation. It does not say “the Senate has power to try impeachments against sitting officers.” Given that the impeachment of Mr. Trump was legitimate, the text makes clear that the Senate has power to try that impeachment.
Read the rest of his analysis here.