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You may NOT have solo 401k for your employee - even your spouse was your employee.In this case - if your spouse was self-employed - she might be eligible to set a solo 401k for herself. In this case - that might be done by her estate or personal representative since she passed away.
The issue is NOT that you may have the solo 401k - but that plan is for YOU only - and not for your spouse even your spouse is your employee.So all references are correct - but still you may not make contribution for your spouse with YOUR solo 401k.
As that is a single member LLC - I assume - all income and deductions are reported on YOUR schedule C.So for your spouse - to be eligible for contributions - your spouse must have separate self-employment income.OR - if your spouse is your employee - you will set a retirement plan for her - but that woudl not be solo 401k plan in this case.
To be eligible to participate in the 401k plan - your spouse should be your employee and should receive wages - that is teh issue.
So - your LLC - assuming a single member LLC and classified as disregarded entity - so you report your business income and business expenses on schedule C.
Then - you establish a solo 401k plan under your LLC using EIN assigned to the LLC.
Then you have your spouse as an employee of that LLC - and because the LLC has an employee - it must file employment tax returns and remit employment taxes to the IRS and state authorities.
Then - your spouse may do elective deferrals from wages and contribute to your solo 401k plan that you establish.
That contribution is reported on W2 form.
As your spouse passed away - all issues are handled by the personal representative on her behalf.
Otherwise - there is no difference - she still have to be an employee of your LLC.
Let me know if you need any help to establish a plan.