1. Download the latest version of the fan translation and extract it.
2. Make this folder path on your SD card: SD:/luma/titles/TITLEID/romfs.
3. Replace TITLEID with one of the following as it depends on the version of if you are playing:
JP Birthright: 000400000012DC00
JP Conquest: 000400000012DD00
JP Special Edition: 000400000012DE00
4. Move the files from FireEmblemIf_EnglishTranslationPatch_4.1.zip/Patch/rom to your romfs folder you made in step 2.
5. Put your SD card back into your system, press and hold Select when you boot your system, and enable "Enable game patching".
6. Start your game and you should see the English patch in action.
Yes this works on digital/downloaded versions as well.