Alexander's heart cheered at the promise of the two letters by Lady Nanazin, easily knowing it would be a great boon for him.
The one addressed to the Queen Mother was sure to have a much more decisive impact than Alexander's lone attempt, thus successfully subduing Ptolomy, and perhaps even getting him on his side.
The regal lady might even help douche some of her husband's flaming anger towards Alexander in this way.
But the much bigger impact of Lady Nanazin's letter would surely be the second one- the one urging Mikaya to soften her father towards the marriage deal.
If the favorite Matrak Princess were to intercede on Alexander's behalf, combine that with Azira and Azura's own insistence…. the man figured he could get away from the marriage with minimal investment.