Every time I would take a picture with my Android LG-V30 cell phone and then send that image to a friend or family member, using the Gallery share function, the image would NOT be sent.

When viewing the photo you just took in Gallery, you will see a number of menu options just below the image you just took.  The menu items are as follows:  Memo, Related, Edit Share, Delete.  The menu I use to send my photos to a person is Share.  When I choose Share a new screen pops up with the title “Share via.  Tap to send images, music, videos, etc to nearby devices wirelessly”.  Below this screen menu are icons showing small images of my most popular people that I communicate with and below that are a huge selection of applications you can use.  

I always choose the icon images of family and friends and seldom go down to Messaging or Email choices.  But this would fail to work until I made the following change.

Solution:  Settings > General > Apps & Notifications > App Info. > Gallery > Data Usage > (Turn this next setting ON) Unrestricted data usage.

This worked for me.  I know it did because shortly after sending my first image I got a quick thank you response from the person I sent the picture and text to.  Also, the image and my text, that I had just sent, kept showing in Messaging application and did not disappear.