What was the name of the person deputed by the local ruler to record whatever stories Ibn Battuta dictated after returning to Morocco?

Ibn Juzzay

The correct answer is Option 1 - Ibn Juzzay

Ibn Juzzay was deputed by the local ruler to record whatever stories Ibn Battuta dictated after returning to Morocco.

This is what Ibn Juzayy, who was deputed to write what Ibn Battuta dictated, said in his introduction:

A gracious direction was transmitted (by the ruler) that he (Ibn Battuta) should dictate an account of the cities which he had seen in his travel, and of the interesting events which had clung to his memory, and that he should speak of those whom he had met of the rulers of countries, of their distinguished men of learning, and their pious saints. Accordingly, he dictated upon these subjects a narrative which gave entertainment to the mind and delight to the ears and eyes, with a variety of curious particulars by the exposition of which he gave edification and of marvellous things, by referring to which he aroused interest.