This was specifically for the Galaxy Note 3, but I am posting it here for the possibility it may be helpful for other Android Phones besides this one. While viewing the HTC One, Galaxy S4 and other pages I saw many people were experiencing Picture and Group (MMS) messaging problems. Obviously the steps may vary slightly depending on your specific phone model but I believe the APN settings should be relevant? If your phones APN settings differ from what is written below, retain your APN setting and only change the two lines that corrected the issue for my new phone.
This is how I fixed my Note 3 from not sending or receiving Group Messages and Picture Messages while connected to WiFi. My phone would not Activate Data to send or receive those while connected to WiFi, resulting in error. The message or picture would try to download but would fail or would not send.
Copy/Paste from my original Discussion.
After two months I have found a solution to Group and Picture messages not being sent or received while connected to WiFi.
It involves the Phones APN settings and was a very easy fix.
Go to /System settings/Connections/More networks/Mobile networks/Access Point Names. Here you will see the APN "T-Mobile US LTE" Click this and copy down all of the information. For the Note 3 it should say
Name - " T-Mobile US LTE "
APN - " fast.t-mobile.com "
Proxy - Not set
Port - Not set
Username - Not set
Password - Not set
Server - Not set
MMSC - " http://mms.msg.eng.t-mobile.com/mms/wapenc "
Multimedia message proxy - Not set
Multimedia message port - Not set
MCC - " 310 "
MNC - " 260 "
Authentication type - Not set
APN type - " default,mms,supl "
APN protocol - " IPv6 " <----------------This is what I changed
APN roaming protocol - " IPv4 " <--------This is what I changed
Turn APN on/off - " APN turned on " checked
Bearer - " Unspecified "
Mobile virtual network operator type - " None "
Mobile virtual network operator value - " Not set "
Under the list of "APNs" at the bottom of the screen you see a "+" sign. Click that and created a new APN using the same exact Settings as the "default" TMO Note 3 APN. But you are going to make a change to theAPN protocol and the APN roaming protocol. For both of those you are going to change to " IPv4/IPv6 "
As soon as I created a new APN and used IPv4/IPv6 for both of those my phone was able to send and receive picture messages and send and receive group messages while still connected to WiFi. I tested this a great deal. I even tested it on different public WiFi.