I'd probably word it a bit differently, i.e. change the verb to a noun, but I think you've got the gist. Here's my rendition:

"We shall effect the final settlement of the employment relationship by 30 April 2006."

In this particular case, I ignored "unverzüglich" because the exact date is given, i.e. it doesn't really matter whether they do it quickly or not, as long as it is doen by the 30th.

If you feel uncomfortable about leaving that off, I would recommend using something like "quickly" or "without delay" - I feel that using "immediately" as a translation for "unverzüglich" would be going too far.
:-)

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Note added at 19 mins (2006-05-05 10:12:01 GMT)
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Correction: "...done..."
;-)

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Note added at 22 mins (2006-05-05 10:15:05 GMT)
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Okay, I looked at it again and my addition of "we" might also be going too far (it depends on the context) - it's just that I prefer active sentences. A passive sentence would probably work too:

"The final settlement of the employment (relationship) shall be effected without delay by 30 April 2006."
;-)

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Note added at 23 mins (2006-05-05 10:16:30 GMT)
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BTW - If you don't like "(to) effect," you could also use "carried out," "completed" or even "done."