My background is more LEV...

As you mention the new parts have been ordered and tested to show that it is working then that would be sufficient, provided the testing meets the accepted guidance / standard and the person performing the testing is competent.

Whenever we change carbon or HEPA filters these are always tested by the engineer to ensure they working as expected, even something as simple as fan speed would need checking to ensure a minimum 0.5m/s face velocity.

Further to what Kate said:

Have a look at Reg 9 of COSHH and the relevant  part of the ACoP. Essentially this says  that there must be evidence that any controls that you decide  use to control expose to hazardous substances actually work. The reg does not  spell out what this evidence consists of; it is down to you to decide if it is good enough. So the people who fixed your LEV  say, now it works; do you believe them, taking into account that you trusted them to  do the works? If so, go with what they say.