Typically, employees are offered the opportunity to open an HSA account through the HSA provider that is selected by their employer. However, because each account is tied to the individual, you can move your HSA to any provider who offers the solution (such as Lively). Individuals who may get their health insurance through an exchange or marketplace can open an account directly with any HSA providers who allow it (e.g., Lively).
Source: "Publication 969 (2018), Health Savings Accounts and Other Tax-Favored Health Plans.”
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