Desea utilizar funciones de ventana para esto, en lugar de group by
:
select FromUser, ToUser, Message, [Date], UserId, UserFullName, UserName, UserPhoto
from (SELECT CM.FromUser, CM.ToUser, CM.Message, CM.Date, U.UserId,
U.UserFullName, U.UserName, U.UserPhoto,
row_number() over (partition by CM.FromUser, CM.ToUser order by [Date] desc) as seqnum
FROM ConversationMessages CM INNER JOIN
Users U
ON U.UserName = CM.FromUser
WHERE CM.ToUser = @user
) s
WHERE seqnum = 1
ORDER BY CM.Date DESC ;