As of today, I've got an "app" on the Google Web Store. It's a Chrome extension that does one thing: moves you from an IMDb film detail page to its corresponding Letterboxd film detail page.
Aptly titled, IMDb to Letterboxd Redirect is about as simple as a Chrome extension can get. Working entirely in the background, it checks that the current tab is a film detail page on either site, does some url string magic and pushes you to the other. This first version also works from Letterboxd review pages.
Who needs this? I don't know. I find myself jumping between the two on Desktop a lot. And while there is a button on Letterboxd's film detail pages to go to IMDb, the same is not true the other way around. Now there's a button for that.
I may expand the functionality to include more shortcuts to various features not easily accessible from the UI, but for now this does one thing reasonably well. Let me know if you use it and follow me on Letterboxd!