No. An active STON staking position cannot be transferred or reassigned to another wallet.
When you stake STON, you receive an ARKENSTON NFT that represents the position. ARKENSTON is a soulbound token (SBT), so it cannot be sent to another address or have its owner changed via a normal transfer.
Early unstaking is also not available — staked STON stays locked until the unlock period you chose when you created the position ends. See Is it possible to remove STON tokens from staking before the end of the unlock period?