No. Keep both. The original shows what the employer stated at the time of hiring, and the reissued letter shows the same offer confirmed by someone still in place. Discarding records makes any later inconsistency harder to explain.
Preserve the sequence, do not rewrite it
If the reissued letter differs from the original in duties, title, salary, or dates, that difference should be explainable by something real, such as a restructure, rather than by editing. Note the reason in the file. Resist the temptation to improve wording that was accurate; a rewritten duty description that no longer matches the actual job creates a larger problem than the one being solved.
Reviews of two-letter files usually stumble on the dates, not the duties. The original carries one signature date, the reissue carries another, and nothing in the file explains the eleven weeks between them. A single dated note from human resources naming the departure and the successor’s appointment closes that gap, and it costs one email to obtain.
File the note between the two letters. The legal point behind the housekeeping is narrow: the documentation evidences an arrangement the employer made, so an unexplained substitution invites a reviewer to ask which version the employer actually stands behind. Hypothetical example: a corporate treasury team keeps its original letter for a Management Consultant engaged on a financial reporting rollout, adds the reissue, and attaches a two-line memo giving the departure date and the successor’s appointment date.