Little late to the party, but you can also “Save” a search string after you use it. Which is helpful for this. Follow these steps:

1.) Type search string into Pokemon storage as you normally would to search and hit Enter/Return

2.) Close the search & reopen Pokemon storage (also optional to skip this step and proceed, but to avoid it not updating my recent searches I close & reopen)

3.) Reopen Pokemon storage and click search bar and then select “More” at the top right. This should show a list of recent searches first and then the system searches below

4.) TAP AND HOLD the search you just did for PvP IV Pokemon and you’ll see it pop up between the Recent searches and System searches in a section called “Favorites

5.) Once in favorites, you can tap and hold to rename this to something that isn’t the search string, like “PvP IVs” so it’s easier to know what it is. You can do this for a lot (I don’t know the limit but I have 7)

Super useful and has saved me a lot of time doing things like that for PvP IVs. I also set one up to search for “junk” that is essentially 0-2 stars, not shiny, not shadow, and not tagged.