A QGIS plugin for move all selected features from layer and snap it to another vertex.
Download the zip file.
Extract it in your QGIS plugins folder.
On GNU/Linux, probably: /home/USER/.qgis2/python/plugins/
On Windows, probably: C:\Users\user_name.qgis2\python\plugins\
Change the name of the extracted folder to "MovewithSnap".
Start your QGIS and go to Plugins->Manage and Install Plugins.
Type "MoveWithSnap" and check the plugin.