What is the ruling on sending the number of the preserved pages daily in a WhatsApp group for the purpose of encouraging memorization, and does this fall under the category of showing off, knowing that not sending it may lead to laziness or abandoning memorization?

There is no objection to cooperating in memorizing the Holy Quran in this manner, as it falls under the rubric of cooperating in righteousness and piety and enjoining one another to truth, provided there is sincerity of intention to Allah and caution against the whisperings of Satan. There is also no objection to sisters encouraging each other to memorize and reminding one another, nor to informing the memorizer that she has completed what was requested of her to memorize, as long as they are keen on sincerity and avoiding ostentation.