Can I run isolation forest on existing data to find anomalies, save it for the future and use it on incoming data?

One of the major arguments I had recently is if we can save an unsupervised learning model to disk and use it later on incoming data. Isolation forest is one of the models that I use a lot for unsupervised anomaly detection and I always save it to a disk to use on future incoming data. Is it theoretically wrong to do this?