He does keep copies in the transporter buffer!
For security purposes calling it a trace... I know, plot device, but I thought it was funny, let me know if better community to discuss :)
Star Trek TNG, Season 2, Episode 7 - Unnatural Selection, timestamp 28:43 on mine.
Main characters actually often die in TNG. But chief always has copies on hand.
O'Brien's 3-2-1 backup game is strong
O’Brian: “Some of you people are cool, don’t go on the away mission tomorrow.”