There are ways to transfer a withdrawal from one annuity to another as a 1035 exchange. There are some specific rules about what can be done so you should get some tax guidance to make sure you follow them.
Here is what investopedia says:
A 1035 exchange is a provision in the Internal Revenue Service (IRS) code allowing for a tax-free transfer of an existing annuity contract, life insurance policy, long-term care product, or endowment for another one of like kind.
