The Christmas Story episode (1967)
I am watching the episode from December 1953, The Big Little Jesus, on DVD.
The 1967 episode The Christmas Story, is a direct remake of The Big Little Jesus.
In the 1967 version, Bill Gannon is Joe's partner while in 1953 it was Frank Smith, but the dialogue between the two is almost exactly the same. The other character names are all the same also.
Two actors from the 1953 episode reprised their roles for the 1967 version, Ralph Moody plays the pawn shop owner and Herb Vigran is the hotel desk clerk.
In 1953, chief suspect Claude Stroop was played by James Griffith. In 1967, Bobby Troupe played Stroop.
As far as I know, this was the only direct remake from the 1950s episodes that was done in the 1960s version.