with the kind of inverter you would need to move the machine and lift
it would be less expensive to just replace the battery

also if it is a sitdown or standup forklift it should have one very large battery(2-3000 lbs or more)
if youre referring to the individual cells they combine together to make one battery
changing these one at a time would put added stress on the rest of the old cells and cause them to fail rapidly

by the time youre done with all the old cells (swapping them out) the 1st ones you replaced will most likely now be damaged

also you could expect to pay twice as much as a replacement by piecing it together like that

only pallet jacks would come with multiple batteries (four six volt golf cart batteries)

never swap cells unless the battery is new and under warranty

also dragging a 240v or 460v cable behind the machine would definitely be cause for concern in itself
such as a short circuit fire hazard by dragging the cable or getting it snagged on something or someone

and before you say "theyre careful its not a concern" i just like to say what i tell all my customers with Mcguyver ideas
"thats why they call them accidents not purposes"

but with a modification like this
YOU WOULD BE HELD SOOOOOOOOOOOOOOO LIABLE IF SOMETHING HAPPENED
as the technical advisor to them or the mechanic preforming the install you can be held liable if something BAD happened as a result of your work separately from your company (if youre not self employed) (IE they name both you and your company separately in the lawsuit)
recommend against it