I don't know why not. Unless the stock/fund/ETF/etc. was something very obscure, a penny stock, or something along those lines that the new custodian does not offer, then you shouldn't have a problem investing in the same stock in your IRA. Usually, an IRA will give you many more options than your 401k, as the 401k is usually limited to between 10 and 30 investment choices. That being said, there is no way to know for sure without knowing what the stock is and who your new custodian is.
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