How to replace brake lever from integrated shifter?
I don't know the answer to ST-EF50 in particular, but usually the lever blade (the part that broke here) is indeed able to be mechanically removed and reinstalled, given the willingness to go that deep with disassembly. However, Shimano doesn't sell replacement lever blades for many or any brake levers anymore, and definitely not the more entry level ones such as this. If you were able to replace it, it would tend to need to be an exact matching part; there's nothing like standardization for this. So that suggests that if you are able to replace it, it's going to be by way of a blade scavenged from another of the same unit. The good news is that ST-EF50 is one of if not the most populous flatbar such part from the last decade or so, so a lot of shops that keep broken shifters and derailers for cannibalization may have one in a bucket somewhere.