Get Text2Store.
Free to download and try. Backing up and searching are free forever; reading every conversation in full and exporting need a one-time purchase, and one purchase covers every iPhone, iPad, and computer you own. See pricing.
Questions to hello@text2store.com.
Next
Plug in your iPhone or iPad, tap Trust, and click Back Up. The first backup takes a while; every one after it copies only what changed. Read the two-minute guide.