How to expedite access to a deceased family member's iPhone?

I am sorry for your loss. We have been there and understand the difficult times. Unfortunately, there is no set time that Apple specifies to respond to requests like this, but judging from other posts, a month is usually about the time that it takes for Apple to make a decision.

Unfortunately, there is a very important detail that is easy to overlook while looking at Apple's documentation. Here is the pertinent information:

While we may also be able to help remove Activation Lock from devices that use your loved one’s original Apple Account, their iPhone, iPod, and iPad will need to be restored to factory settings before they can be used with another Apple Account. Please note that devices locked with a passcode are protected by passcode encryption, and Apple can’t help remove the passcode lock without erasing the device.

Most of the time, the phone has been Activation Locked, and that message appears on the screen. Apple can help with removing the Activation Lock, but if the user was using a passcode to get into their phone, you will need to know that passcode to get at the data on the phone. In other words, Apple cannot help with the passcode.

Hopefully, someone will remember that passcode that was used on the phone.

I am unfamiliar with the SSL code that you reference but the process is outlined at How to request access to a deceased family member’s Apple Account - Apple Support

in the United States, you need a court order as noted in the instructions or a legacy contact key. Other jurisdictions may have different requirements.

Re: “There is important information that I need off his device, for example, his Will and his funeral policy details. I must have these details to carry out his last wishes.”

I hope the will is somewhere other than the device. You need to submit the will (if there is one) to the court before they will appoint an executor.

Until the court appoints an executor and you have official documentation to that effect, Apple might not be able to help you get into your loved one’s Apple Account. In any event, if the phone is passcode-locked and you do not know the passcode, the only way back in might involve resetting and erasing the phone.

I'm sorry for your loss and understand your frustration. I know this will not assist you now, but as others read this thread, there is something that may have been overlooked and others may wish to make themselves aware of this and perform these steps to help their loved ones access their devices. See this Apple Support document regarding the creation of a Legacy Contact to ensure accessing their loved one's devices. How to add a Legacy Contact for your Apple Account - Apple Support