Sure, here are some screenshots.
My favorites, notice the profile and the width.
Selected first (steel) favorite and made a beam. Notice the width and profile, (the last beam I drew before had a different width but this profile, it seems only the width transfers). Then selected second favorite and drew a beam, same profile but the width changed (so the favorite selection was successful at least).
Manually changed the profile and drew a beam. Then I picked up from the steel beam and injected into one of the others, only the width changed, not the profile.
So it seems the profile does not get changed with favorites or pickup/inject. I've checked my element transfer settings and checked to transfer everything for beams, makes no difference.
| AC 25 Int | Win10 | i7-7800X | 32 GB | GeForce RTX 2060 6GB |