You can transfer money between accounts but stocks/shares/funds have to either be bought and sold or removed and added to achieve the same thing.
It's perhaps not a very common requirement but I just needed to do it between two pension pots at the same provider.

I filed a wishlist bug for this some time ago. It will eventually get done, but probably not until there is a major revision of the overall handling of investments within KMM, which will probably also include being able to hold cash in investment accounts without needing a separate brokerage account.