Azlan has presented two ideas that are both good.
If the push is one that you should take over the table, if it is short enough so that it almost bounces twice, it would probably be easier to take with the backhand. But if it is coming off the end-line, even if it just comes off, you should be able to take it with the forehand as well.
Either way, if you are taking forehands from the backhand side, the footwork to move from deep on the backhand side to deep on the forehand side is worth practicing. Here are two versions of that.
This first video uses a cross step to get there and the unique thing about this cross step is that the way the guy demonstrates it, you can end up with both feet on the ground and your feet uncrossed when you take the stroke, or just after, so you can get back into position. The way they show it, they are taking taking the stroke while the foot is crossed and than they get the other foot down to get back into position. But in playing with it, I have found that I can make the cross smaller, get the lead foot down and in position to take the stroke from deep in the forehand with both feet on the ground. With a step like this, you can cover a lot of ground very quickly.
Here is another video where Xu Xin covers the ground from deep on the backhand side, all the way over to deep on the forehand side with just a regular one-step, it is a large one-step and he has long legs, but he never has to cross his legs to get there.
Xu Xin's footwork is ridiculous and I could watch that video over and over again, but working on these footwork exercises, even without the ball, just shadow drills, can help a lot. I do footwork drills alone at a table sometimes. But I also like doing them in front of a mirror because that actually makes it much easier to correct your form and improve weight transfer and stroke at the same time while practicing the footwork.
And doing shadow footwork drills has definitely caused my level to increase more quickly then it would have if I did not do them.