How can I bring objects through to another slide based on state?

I think Nathan is right he over complicated it. His initial statement of using three variables is best, you would just create logic to set and unset the values based on if they are selected. I would do it on the next/previous button as it could get complicated otherwise

Each slide is like its own webpage, so one slide can't really access objects from another slide. However, you could try a few options.

1. The slide master, and its layers, can display on any slide. The master slide displays below your current slide objects, while the master slide's layers display above. You could make layers on the slide master, each containing a single statement, and then set up triggers on the slide master that could display one or more of those layers. Set each of those layers to not hide other layers. That way, they can all be visible at the same time. This approach would be good if your statements are complex, including text, shapes, images, formatting, or animation.
2.  If your statements are just text statements with basic formatting, you could assign each statement to a text variable. Then, on your final slide you can display all of the relevant variables inside a set of text boxes using the %{variable name}% shortcut in your text box string.
3. You could also track the selected statements with variables and reproduce all of the possible statements on your final slide (in layers or on the timeline). Based on the selection variables, you can then make the statements visible as layers or unhide them on the timeline for display.

If you have 18 variables m(statementText_#) each with a text statement, and three selection variables (statementSelection_#), then use triggers to identify which was statement was selected and then copy the corresponding statement variable to one of the the selection variable. Selecting multiple statements on one slide and saving only three might get messy with only triggers. Maybe you can set a T/F variable (isSelected_#) for each statement (all starting as false). Set to true when selected. Use a trigger and variable (numberSelected) to sum the total number of trues. If they exceed three, then set a variable (T/F selectionAllowed) to use as a conditional to prevent further selections. On your reporting slide, check each of the isSelected_# variables for true, using the current value of the statement Selection_# variables to determine which variable to assign the text value to. 

This may be overcomplicated, as it was stream of consciousness. You can probably streamline it. Or, you can adjust the way users select statements to make tracking them easier (may be a better option).

I have managed to figure it out and its working perfectly! took a while but got there in the end.

I set up a variable to each statement to select. I then set up the Select 1, 2 and 3 to display the outcomes. I used variables to display the statement in selection 1 if the option was set to selected, but if none others were selected. Then option 2 and 3 were set if the statement was selected, the variable was currently blank, and it wasnt the same as selection 1. and then did the same for selection 3. Lots of triggers and variables but it works perfectly for what I need.