💡 Detailed Explanation
The correct choice is 'いただき' (from 'いただく' - humble form of 'もらう' - to receive a favor from a senior). The grammar pattern '[Verb Te-form] + いただく' indicates that the speaker humbly received the favor of a senior doing something for them. Sentence translation: 'I humbly had Professor Yamada write a letter of recommendation for me.' 'さしあげ' is giving to a senior, 'ください' is asking them to do it (would be '書いてください'), 'やり' is giving to animals/juniors.