Can you use "must" to replace the following cumbersome phrase?

E.g. Can this sentence:

"The IT company that is hired to run OPTN's computer systems _would have had to have_ worked on an organ transplant network in the past"

be shortened to:

"The IT company that is hired to run OPTN's computer systems _must have_ worked on an organ transplant network in the past"

and still retain its meaning?