If it is a general letter of asking reimbursement through the official chain, then it is not needed to write address and any salutation. It can be started directly with the subject matter.
The sample letter is given below.
The following miscellaneous expenses were incurred by the undersigned.
Type of expenditure: Lunch for officials
Approval may kindly be accorded for reimbursement of the sum of $20.00 to the undersigned under clause XXXL034.
XXXXXXXX (Name of The department and Organisation)
Enclosures: Bill of the Hotel etc.
Designation and Department name ( of Head of the Department ) ____________________.
Designation Finance Department ( of Authority of Finance Department ) ____________________.