State the actual duties, relevant knowledge and factual business circumstances. Keep unsupported loss estimates and claims of sole expertise out of the explanation.
Use facts that can be traced to evidence
Identify relevant prior work, the applicant’s contribution and the proposed response. A concise accurate account is more useful than dramatic language that leaves the employment or knowledge requirements unexplained. Explain specifically why personnel already at the destination cannot perform the work themselves, since a staffing shortage on its own does not show that the applicant's particular knowledge, rather than simply additional labor, is what the situation requires.
Tie the urgency to a specific triggering event, such as an unexpected system failure or a client escalation, and describe the sequence that followed rather than asserting pressure in general terms. Note what internal options were considered and rejected before requesting the applicant's transfer, since a documented decision process carries more weight than a letter that jumps straight to the conclusion. Keep the account of the applicant's prior involvement limited to work that actually connects to the present assignment, so the letter reads as a continuation of known expertise rather than a justification written after the fact.
A dramatic account of loss avoided says little without records showing what the applicant actually knew and did during the response, so let the factual account carry the weight rather than the language chosen to describe it.