Cut it into page-height slices in the phone editor, leaving a small overlap so no line is lost.
Select the slices top to bottom; the list order becomes the page order.
Confirm nothing vanished between two slices before deleting the originals.
Scrolling screenshots are typically 1080px wide and ten thousand pixels or more tall. As a PDF that is a single page with an extreme aspect ratio. It opens, but printing scales it to one sheet and the text becomes unreadable, and many viewers render it as a thin strip.
The reliable route is to split the screenshot into several images in the phone editor, then convert those in order. The result is a normal multi-page document that prints and reads correctly. Converting first and cropping later means doing the conversion twice.
For chat records, receipts or a long web page kept as evidence, a single tall page is correct: nothing is cut and the sequence is unambiguous. Decide from the purpose, since printing and reading want pages while archiving wants one continuous image.
A 1080x12000 screenshot is roughly 1-3MB as PNG and converts without resampling, so text stays sharp. It also stays large: if the file must be sent, compressing afterwards will soften exactly the small text the screenshot was taken to preserve.
An A4 sheet is 210mm wide. Stretch a 1080px image across it and the effective resolution is around 130dpi, which is where body text stops looking crisp, because a screenshot is laid out for screen pixels rather than for print. The honest expectation for a converted long screenshot is readable on screen, not readable on paper. If paper is the point, re-export the source at print resolution instead of tuning the PDF afterwards.
Yes, and that is correct for archiving. It is wrong for printing.
No. The image is embedded as-is, so the file simply stays large.
The conversion follows the file list order, so add the slices top to bottom.