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Yes you can do this. There is a component called "location sensor" which will do the trick. As noted in the link below, your Android-based phone/tablet must have location sensing enabled through wireless networks or GPS satellites (if outdoors).
Then to send the information to another person, my recommendation would be to use google Firebase as takes care of data sharing via the cloud. This option allows two or more phones to share the data with minimal coding. There is another component available for this (look in palette category "experimental"). Otherwise you can POST the location information to a web service / database using the "web" component (found in the "connectivity" palette category).
Another free to use alternative to MIT App Inventor is thunkable.com. Might be worth looking at as has nice mapping capability and offers IOS support.