It appears that there is no option for friends to actually use Gravity Trampolines. When using the "Find Teleport" button in the fleet tab and selecting the Trampolines that are to be used for teleport, you are directed to the 'Fleet' page where you select ships and send them into defense at the same coordinates as the Trampolines. When they arrive however, there is no way to send them through the Trampolines. When using your own trampolines there is a switch to select "Send Through Trampoline".. this is missing for friends, thus they cannot use the trampoline at all..... even though both are on the same coordinates in defense and the trampoline has been opened to friends. (Note: Both the Departure and Arrival Trampolines are in position at this point, ready for use).
 Also, this applies when sending a fleet from coordinates to a trampoline. It cannot be used upon arrival regardless of the position of either fleet or the Trampolines.
 
 Has anyone else encountered this problem? If it is indeed a bug or problem in game, could it get fixed please. 
 
 
-----(The introduction of the "Send Through Trampoline" switch has made it much easier to use the trampolines.... a good addition to the game.)

 Apologies. This rightfully belongs in the "Bugs" section. 

I have experienced this as well when I tried to use a friend's trampoline. Now that I have my own I've noticed that if you open all the details of the gravity trampoline units they have an option to allow friends to use them which was, by default, not turned on. I turned mine on but have not tested them yet but that may fix it.

As I said, the Trampolines were already open to friends. The option to utilise them is not there when it is a friend using them. There is no button to select "Send Through Trampoline".

Try to trick the game.
If there's a special page with a distinct link to do this (I unfortunately don't have experience with trampolines) you may type the link directly into your browser and like that you've overcome the missing button. This should be possible if you are allowed to use them.

 I appreciate the advice but there is no "Special Page" to do this. It is done in the fleet page as per sending a fleet. Thus the link is the Fleet Page link. There is no other. 
 I have already explained, twice, that it is a missing button. That is all. The button allows for the selecting of the Trampoline and recalculates the gas and time needed for the flight. When you use a Trampoline you will see that there is no other way to do this.

Admins stated that they changed it so friends can only provide the destination tramp, you must own your starting tramp.

Yes. I was notified when admin answered my post. The issue was resolved in bugs, as I am sure you have seen. Thanks.