Any person who, on the day preceding such person’s date of transfer pursuant to this chapter, held a position compensated in accordance with the Executive Schedule prescribed in chapter
53 of title
5 and who, without a break in service, is appointed in the Department to a position having duties comparable to the duties performed immediately preceding such appointment shall continue to be compensated in such new position at not less than the rate provided for such position, for the duration of the service of such person in such new position.