As kendallpark pointed out this is highly unlikely. I upvoted you because it's an interesting "hmmm... what would it take?" The spatial resolution of an fMRI is high compared to something like EEG, but the time resolution is much slower. Even the spatial resolution is on the order of cubic mm at the absolute best. So, we are no where close to being able to scan the activity of every one of the ~100 billion neurons in a human brain and it would 7+ orders of magnitude better spatial recognition and associated processing capabilities. So, the magnitude of your "if" is large enough that it's on the level of Kurzweil Crazy, but cool to think about regardless.

I know nothing about neurology, but my money would be on using a different mechanism to extract all the data, maybe something like fake neurons that dump all the information via WiFi, a MITM attack for the brain itself if you like.

With our current understanding, such tasks are comparable to trying to break the speed of light. However, we could probably get incredibly close without any internal data extraction. Our personalities, while highly complex, can be approximated into some simple traits (e.g. 74% 'passive-aggressive', 47% empathy) and replication of our knowledge isn't strictly necessary. Find 10,000 interests and create a int_8 each of how much someone is into it. Et cetra.

I highly doubt this will ever be possible, from both a biological and a computer science standpoint.

I don't think we need to scan 100% of the brain in molecular detail in order to read & preserve the information. It should be possible to observe the circuitry at a higher level and recreate an approximation -- though it'd be just that, an approximation. Additionally, much of the information could be compressed to a much more lightweight format than digitizing the physical neural networks of the brain.

Digitizing a static physical model of the brain is problematic in itself. Many regions and structures in the brain are likely structurally dynamic. That is, the neural circuitry could change structure from day to day and this is definitely true over longer timescales. So it'd be much easier to read the data from the brain into another format rather than emulate the physical structure of the hardware.

I've thought a bit about information could be read from MRI scans such as these. In the absence of higher resolution data, I don't think there could any memories retrieved. I don't know the low-level details of how MRI data is encoded, but I do know it is recorded in slices. To retrieve memories, you'd need to read 3D regions from the brain. And it'd need to be much more high-resolution.