The general rule is that you do have to surrender your license. However, the FeV allows officials to make exceptions at their discretion.

If you surrender your license, the office will generally keep it and you can exchange it at any time you want.

However, as I said before, if you have a California driver's license, you aren't able to exchange your license in Germany. You can get a new license with somewhat reduced driver training requirements, but an exchange is not possible.