Writing in India completely disappeared after the Harappan period and did not reemerge until the invasion of Alexander the Great.

The finding

What the evidence shows

There really is a long gap between the disappearance of Harappan writing and the appearance of Brahmi script in India, but tying its reemergence specifically to Alexander the Great's invasion misstates the evidence. Historians point instead to contact with the Persian Achaemenid empire in the 6th century BCE, a century or more before Alexander arrived, plus indirect evidence of earlier literacy such as Panini's grammar, and some Brahmi inscriptions may predate Alexander entirely. Alexander's expedition gets mentioned in sources mainly because Greek writers who traveled with him recorded seeing Indian writing already in use, not because he brought writing back to India.