Can I compress SMS content to free up storage?
The app iExplorer can export one, several, or all messages from your iPhone and save them in a number of ways. Once you have exported and archived the conversations onto your Mac or PC, you can delete them from your phone &amp; reclaim space.



The easiest takes each conversation and exports PDFs out of them with images attached in-line: 



Other options let you save images &amp; other attachments in a variety of ways:



Lowest price point is US$35, and well worth it.

[Full Disclosure: I'm just a happy customer who has no financial stake in Macroplant.]