Trying to select the Cloak of Protection from the dropdown of Infuse Magic Item, for a future Artificer I will play. It's one of the available infusions for Artificers, but it isn't in the dropdown...

Are you 10th level in artificer?

We start our campaigns at L2, so that's what I was when I looked in the dropdown.
I just checked again, making my character L10, but it's still not in the dropdown.
The character is set up in my DM's campaign and he has all the books I think.

Then something else is affecting your shoot or you are not using the correct drop down (you need to use the level 10 drop down), or looking for wrong thing (choose replicate magic item, then choose the cloak in the level 10 list). 

As proven by my test and screenshot it is very much there and working perfectly. It's basic rules so it doesn't matter what sharing your DM has or not. 

EDIT

I made a video to show that it does work and where to find and use it.

Do you have access to the regular magic item Cloak of Protection? If you can't see it via the tooltip link here, then that's why.

Quote from naruhoodie >>

Do you have access to the regular magic item Cloak of Protection? If you can't see it via the tooltip link here, then that's why.

 
It's part of basic rules, everyone has access to it.

Yeah I see it now - thank you Cyb3r