Delay of business expense reimbursement

IANAL, but this (in particular wrt. universities) is a very common difficulty.

There is nothing special in having a public employer here. AFAIK the general procedure for claims that are not paid in a timely fashion applies. The only thing that is special compared to other claims (e.g. a contractor invoicing the university) is that here the other side usually produces the relevant calculation, while you hand in data only.

is there a time period in which an employer must reimburse business expenses?

This ask-a-laywer site/case is spot on (even though > 10a old). It essentially says:

• Reimbursement claim has to be processed within a reasonable time.
• The lawyer thinks: 7 months without any particular objective difficulties is too long.
• Specifically, "big administrative backlog" is not a reasonable argument for excessively long delays.

Is that time period affected by the duration of employment?

AFAIK, no. And the claim also doesn't vanish when it isn't processed until end of the contract.

Practical considerations

• I've known (public research) contracts ending due to the related project ending soon treated as a reason to process the claim extra fast: after the project end, they cannot access the project's budget for travel costs any more and thus would need to reimburse from their general budget.
  I.e., the travel costs are essentially lost for them because they cannot be reclaimed from the funding agency of the project.

  But it is entirely their problem if this happens.

• I've experienced (many years ago) that travel reimbursement claims took almost a whole year to be processed by a university. Back then when I reserved places at a restaurant for a work-related dinner, the owner immediately said "You're from university? It's cash only, no payment on invoice for the university." Also, I've heard the general finding in businees/freelancing circles over and over again, that universities are among the latest paying customers one can have (plus discussing which tactics work to make them pay. Unfortunately, the best workig ones are not available for employee travel reimbursement claims)

  What may help you is sending them a proper Mahnung with your head of department (talk to them first) and the head of the administration in CC. The Personalrat may also be able to help.

• For the future, you may want to ask for as much advance money as possible.

  This has potentially two beneficial effects: for you the amount they owe is much smaller. Moreover, administrative rules may be much more strict requiring that proceedings where money was advanced must be processed speedily after the event, otherwise they will be in trouble internally.