Yes. A life insurance policy is a contract, and the contract goes where you go. Moving from Oregon to Arizona doesn't change your premium, your death benefit, your loan rate, or your cash value. Nobody re-underwrites you and nobody re-prices you.
The policy was issued under the laws of the state you lived in when you bought it, and it keeps those terms. If your state required a particular free look window or particular grace period language, that's what your contract says, and it says the same thing in Phoenix. Contract terms lock at issue.
Five things do change.
Your address. Update it with the carrier in writing, not just with the post office. Premium notices, grace period notices, and annual statements all go to the address of record, and a mail forwarding order expires after a year. A policy that lapses because the grace notice went to the old house is the most avoidable loss in this business.
Your agent. Agents are licensed state by state. Yours may or may not hold a license where you're headed, and if they don't, they can usually service the existing policy but can't sell you anything new there. Ask directly. If the answer is no, ask who they'd hand you off to.
Guaranty association coverage. Every state has one, and it's the backstop that pays if an insurance company fails. Coverage generally follows your state of residence at the time the carrier goes insolvent rather than the state where you bought the policy, and the limits differ, commonly $300,000 on a death benefit and $100,000 on cash value, with some states higher. Moving can raise or lower that backstop without anybody mentioning it.
State tax treatment. The death benefit is free of federal income tax everywhere. What changes from state to state is estate and inheritance tax. A handful of states tax estates at thresholds far below the federal one, and a couple run inheritance taxes based on where the person who died lived. Move from a state with no estate tax into one with a $1 million threshold and a policy you own on yourself just became part of a taxable estate. That's a conversation with an accountant in the new state.
Your beneficiary designations, if the move came attached to a life change. Most moves do. A new job, a marriage, a divorce, a kid heading off to college. The beneficiary form outranks your will, and a move is a reasonable excuse to pull the forms out and actually read them.
One thing that doesn't change is access to your cash value. A policy loan is a contract right rather than a state-licensed product, so you request one the same way from the new address, and taking your first policy loan, step by step is the same process in any state.
Do the address change the same week you have the new address, and while you're in the carrier's portal, check that the email and phone on file are current too. Then put the policy number and the carrier's service line into whatever file the new house keeps important papers in, and tell your spouse where that file lives. The policy paperwork to keep, and where to keep it lists what belongs in there.