Parent passed away this past April

[CJM5]

His taxes still have to be done for 2024. I am the executor of his will. Can I do his taxes and sign off on them and send it to the irs?

[ClarissaA1]

I am sorry you are dealing with the death of your father.  Acting as the executor after someone dies can be a stressful job, and often thankless.  You are correct  -- you will need to file a final return for your deceased parent for 2024.  
Your father's tax documents will arrive in early 2025, and you will want to keep track of those documents so you can prepare the final return for your father's estate.    As the executor, you will sign the return for the deceased taxpayer and electronic filing is still available in most cases.   You will need to attach a copy of the court documents that appointed you as the executor to the tax return when it is filed.
If your father has a surviving spouse and files a joint return, the spouse can still file a joint return for 2024.  
Tax Tips - Death in the Family 
Signing the return - Deceased taxpayer