How much does it cost to have an attorney write a letter to another attorney requesting transfer of my will?

The cost depends on the attorney.  But you may want to keep the Will yourself, whether in a fire proof safe at home, a safety deposit box or (if this works in your locale) with the county clerk.  In that case, you, not the attorney, can write the letter.   Unless your former friend is an estate planning attorney, you may also want to have the Will reviewed by one.  It may not be valid.