Despite the very sad circumstances, welcome back to the forums.
I'm so sorry for the very sudden passing of the little fellow, may he rest in peace.
During this time, your family can spend more quality time with the remaining budgie and give him some extra TLC. By observing the budgie's behaviour they will have a better idea on how he is coping and adjusting to the new reality.
If there is not a noticeable change on his behaviour, general activity and playfulness, then all should be well.
The signs to watch out for that something may not be quite right are decrease in activity/singing, lack of interest in playing and even decrease in appetite.
And if this is observed, the booking a wellness check at the avian vet would be the best choice in order to rule out any potential illness.
If later on it is determined that the budgie needs the companionship of a same species friend and your family isn't wanting to add a second bird, then the best choice would be for you to take in the budgie and make him part of your flock.
I'm wishing this budgie as well as your current flock all the best.