She resolved to memorize the Quran but was told to learn Tajwid first

Memorizing the Holy Quran is one of the greatest of blessings, because it is memorizing the words of Allah, may He be exalted, that He revealed as guidance for mankind and healing for what is in their hearts. This decision of yours is a good one, and we ask Allah to help you to achieve the good goal that you want. 

Learning the rules of tajwid is important and will lead to correct pronunciation of the letters, improved recitation and avoidance of errors. But we do not think that you should stop memorizing. Rather you can combine the two and concentrate on reading what you want to memorize first correctly. It is best if you can learn from a woman who reads Quran well. If that is not possible, then use recorded tapes and computer programs for memorizing and learning Quran, and learning tajwid. It is known that the Prophet (peace and blessings of Allah be upon him) did not tell his companions to learn tajwid before the reading and memorizing, but he did tell them to learn the Quran from those who knew it well, such as Ubayy ibn Ka’b (may Allah be pleased with him), Ibn Mas’ood (may Allah be pleased with him) and others. This combined reading, memorization and learning tajwid. 

Most people still memorize it in this manner; they start with memorization, whilst paying attention to correct pronunciation of the letters and learning the proper vowelling, then after they have memorized it or a good portion of it, they then pay attention to other rules of tajwid and the finer points thereof. 

And Allah knows best. 

For information of the virtues of memorizing Quran and the honourable status of the haafiz, please see questions no. 14035, 20803 and 11561. With regard to tajwid, please see question no. 67586.