Answer: B. January 1, 20X1, through May 1, 20X3
Step-by-step explanation:
The management representation letter should cover all the periods that will be in the auditor's report not just the periods that the current management team was in effect in.
Even though the financial statements are for the years ended December 31, 20X1 and 20X2, the auditor has a responsibility to include the events that happened all the way up to the date the reports will be released on May 20X3.
This is why the management representation letter needs to include the entire period of January 1, 20X1, through May 1, 20X3 because those will be in the audit report.