I was reading about IDA* and I found this link explaining IDA* and providing an animation for it

the animation is here

and here is a picture of the solution

I know what is the cutoff condition (it depends on F), and the search is like DFS if the value of (f) of the node is less or equal to the cutoff, and like IDF it is iterative

My question is:

in the animation when the threshold is 7 and after expanding the parent of the goal (14) they stated that a solution has been found, so if we found the goal after expanding a node which is <= the cutoff value can we consider it the solution without applying any condition-test on it?(it's F <= threshold): for example, if there was another level where there is a goal and it can be found with value 13 (less than 14) like the following pic:

when the threshold is 7 11 will not be expanded so we will never get (13)

So, what is the correct solution?

I was reading about IDA* and I found this link explaining IDA* and providing an animation for it.

Here is a picture of the solution.

I know what is the cutoff condition (it depends on F), and the search is like DFS if the value of (f) of the node is less or equal to the cutoff, and like IDF it is iterative

My question is:

In the animation, when the threshold is 7 and after expanding the parent of the goal (14), they stated that a solution has been found, so, if we found the goal after expanding a node which is <= the cutoff value, can we consider it the solution without applying any condition-test on it?  (it's F <= threshold): for example, if there was another level where there is a goal and it can be found with value 13 (less than 14), like the following pic:

when the threshold is 7, 11 will not be expanded so we will never get (13)

So, what is the correct solution?