You can copy and paste the event onto the next map to give it the appearance that it teleported.
If the player can visit the location you are teleporting to before you actually teleport there, copy and paste the event onto the new map, then, in the Event handler screen, click on New Event Page. Leave this page blank (it should not have a graphic). On the first page with all the event actions (whatever your event does), click on Switch X is On (left-side of the screen). Now, in the event that teleports your player, turn that switch On.
What this does is during normal gameplay, the event will not be visible, because it will not have a graphic/commands. The player will never know it is there. When you teleport your player, the switch is flipped and the event will flip to its second page and become active. This makes it appear as if it teleported with the player.