Urgent : Filing I130, I 485 towards expiration of I 94

[Shriya]

Hi Everyone, this forum was very helpful during my previous visa application and we had a good exchange of experiences. Some urgent help is needed. My parents are here on B2 visa and they were scheduled to go back next week, when their i 94 expires. They have been visiting us for last 15 years and have never stayed over.
Just last month my brother got his citizenship and as we dont have any other immediate relatives in India decided to file for GC for my parents. Unfortunately it took a while to get to know the process and we have just completed the package (hopefully). We will be able to send the package tomorrow, but due to weekend, it may not reach the office before Wednesday ,which is the last day of I-94. Anyone has any experience in such cases. My lawyer said it should be ok as they did not have any intent of AOS when they arrived.
What happens if they receive the application right after i-94 expiration? Is there any shortcoming of filing so late? we are filing concurrent alongwith EAD and I 131. How long to get I 131 if need be?
Do we need to send in I 693 with the package or can that be submitted later?How can we prove that AOS was not the intent earlier?

Thanks a ton for your quick responses. Will be very grateful.

[newacct]

It makes no difference if they file before or after their I-94 expires. As they are in the Immediate Relative category, they don't need to be in status to file AOS. Even if they filed years after I-94 expiration it would still make no difference.

EAD and AP take at least 4+ months to get these days.

The medical can be sent with the I-485 or sent later in response to an RFE. Sending it later is mainly done in cases where the AOS is expected to take more than one year, since the medical expires after one year. But AOS in this category doesn't usually take that long, so it may be better to just send it in together.

You don't need to prove anything about their intent. Their intent doesn't matter; they just need to not have lied. Even if they had preconceived intent to immigrate at the time they entered, their AOS should still be approved.