If you had a pillar 3a bank account or fund, then there wouldn't be an issue, because you are not obligated to make payments. However, because you used an insurance policy for your pillar 3a, it is a bit more complicated. The insurance agreement specifies that you must pay regular premiums, and you must give a certain amount of notice to terminate your insurance policy. You have to stick with the contractual agreements. In your case, I assume the typical three-month notice period applies, which is why you can only terminate the policy in October.
The right to use the pillar 3a contribution is based on a calendar year. In order to use the pillar 3a, you have to earn an income that is subject to OASI contributions at some point during the calendar year (2023, in your case). If you earned income in Switzerland between January and May 2023, then you are eligible to contribute to the pillar 3a, and the insurance company has the right to charge you premiums in 2023.
The limit on pillar 3a contributions also applies per calendar year. That means that even if you leave Switzerland half way through the year, you can still contribute up to the maximum pillar 3a contribution, and claim up to the maximum pillar 3a tax deduction.
If you gave up tax residence in Switzerland in May 2023, then you will be liable to pay taxes in Switzerland for the perod from January through to May, 2023. The income you earned during that time will be considered your annual income for 2023, for Swiss tax purposes.
At the end of 2023, Swiss Life will give you an annual statement showing your pillar 3a contributions in 2023. You can use this to claim the pillar 3a tax deduction for your 2023 Swiss taxes.
So in short: Yes, Swiss Life can continue charging you premiums as per your insurance agreement even after you leave Switzerland. The upside is that you can deduct the full amount you pay in insurance premiums (including those paid after you left the country) from your Swiss taxable income for 2023.
