In a word- no

New shifters generally come with a new cable inner. Re using the old cable requires you to completely pull it out at the shifter end. And generally cut an inch off. So unless you’ve got too long an outer you need a new inner every time.

You can leave the outer in place but the inner has to come out.

Not happening. The nipple on the cable is at the shifter end. You don't need to move the outer but the inner needs to come out. You could reusue it (normally possible to get the end cap off) but may as well fit a new one.

Thanks. Will the new one feed back through easily? Cable is internally routed so I’d rather not remove the outer if possible…

If it's continuous outer, or has a guide, yes.

If not, no...

There are many tricks to making it easier though.

As long as you leave the outer in place the inner should just feed back through nicely. A new shifter will have a new cable installed.

Assuming your rear mech is setup properly all you need to do is bolt the new cable into the mech so it’s tight and you should broadly be good to go. Maybe just a slight tweak of the adjuster on the shifter to fine tune.

Cool. Rear mech is tip top currently and I’m a dab hand at indexing, just never changed a shifter…yet!

Cable goes behind the battery and  over the motor so it’s quite a strip down if I have to replace the outer….

it’s a continuous outer though. Tricks you say….???

it’s a continuous outer though.

No tricks needed if the outer is in good condition.
Just slide the inner through.

If the outer needs replacing, you can attach the old one to a new one (end to end, i've used a 12mm long M2 grub screw and lots of super glue before, but i'm sure there are other ways) then sort of "push me pull me" through the frame. Then a bit of trimming and tidying up.

Not all bikes have a continuous outer, or even a sheath to protect the frame from cable rub but, I'd expect an e'bike to have one.

You can always use the old inner to pull the new one through by taping them together at the lever end. Takes very good tape and clean cables though and careful push/pull action to keep them attached.