The best replacement for letter of intent is cover letter.

The best alternatives to letter of intent are rated as following:
★★★★★  cover letter
★★  statement of purpose
★★  personal statement
★★  memorandum of understanding
★  letter of interest
★  term sheet
★  purchase agreement
★  letter of inquiry
★  mou
★  letter of agreement
★  rights of accumulation
★  letter of commitment
★  purchase order
  letter of award
  offer letter
  offer to purchase
  notice to proceed
  letter of introduction

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letter of intent
cover letter
statement of purpose