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Since there is no built-in option of mounting Android device on Mac and browsing Android content directly in Finder, you have to search for third-party app to do this.
With SyncMate Expert you can mount Android device as Mac disk and browse its content (internal and external storages) in Finder window. You can access all folders and files you have on Android, view, copy, edit and manage images (photos, chat images or downloaded pictures), videos, music, downloaded files and any other data stored on your Android.
SyncMate is a powerful sync tool that allows syncing data on your Mac with Android devices - phones or tablets. As mentioned above, SyncMate allows mounting Android devices as Mac disks.
SyncMate comes in two editions - Free (allows syncing personal data like contacts and calendars) and Expert (will sync images, videos, music, playlists, folders with files and more). With Expert edition you can manage text messages directly on Mac.
These simple steps will explain how to manage Android files on Mac.
Besides mentioned above Android devices, SyncMate will sync data on your Mac with iOS devices, other Mac computers, online accounts and storages (iCloud, Google, Dropbox), Windows services (Outlook, Office 365 Home and Business editions).
Find more info about supported devices/accounts and sync options for them here.
SyncMate requires OS X 10.8.5 and is compatible with Android 4.x-7.x devices and iOS 5.x-10.x devices.