Re-using old but good compost?

It will be fine to use for other crops. Make sure that you incorporate some nutrients as the strawberries will have taken a lot of goodness out of it. Well rotted manure or composted waste will be great for most crops, or a store bought fertilizer.

As I see that my answer has been ridiculed by another commenter, I should tell you that I am a professional horticulturalist and landscape designer. Your strawberries will have depleted nutrients vital for strawberries, hence why strawberries should not be replanted in the same soil and should be renewed and placed in a different spot every few years. The suggestion of replacing nutrients is based on more than 50 years of growing crops, including setting up and running an organic market garden and selling the produce.

yes you can use the compost without any problems, it is best to mix some maunure to it as you add it to the new place to add nutrients to it. Also if you have any kitchen waste, especially banana skin put them at the base and tip the compost over them.

I throw my old soil in a nearby city park. They have landscaping trees and bushes, and such, so I add it there. And, since my backyard is concrete, I do this by taking a load out every day. You have a backyard big enough to move your raised bed? How can you not have a place to dump the old soil?

But, do dump it. Especially if you plan to grow veggies. The strawberries have depleted it for as long as you've been growing them. Something is missing from that old soil. I know, I've been growing my veggies in the same soil (container gardener) for years, and the tomatoes and other veggies have become gradually smaller and more disease ridden as the years progressed. Exactly why I'm dumping about 8 liters of soil per day for the last month, and buying more and more new soil. It matters, no matter how much people say "just add nutrients."