Unfortunately there is not much you can do but wait. (I would have suggested reaching out to your MP but you've already done that and your MP can't actually speed up processing).
Since you received a PFL, your application is unfortunately non standard and will likely take longer than normal. If you are asking IRCC to process your application under common law, I assume you have lived together continuously for at least one full year and you provided evidence to prove the one year of cohabitation.
I'm sorry your wife's situation is so unsafe. Is there somewhere she can move to temporarily that is safer? Did you try applying for a TRV at any point?
Tried reaching out to my local MP multiple times and they said the office is not responding to any of there requests. We got a PFL but when the MP asked IRCC about my file they told them that it is a routine process. Even though they know my son has a Canadian citizenship and my wife is currently pregnant in her 8th month. I even sent them multiple articles about what is happening near our home which are online from news agencies like The Guardian, ABC news, CBS and many more.
I wish we had somewhere else to move but when missiles are dropping from the sky and anti-ballistic missiles are being fired from the ground it's hard to move around especially with an 8 month pregnant women and a 4 year old boy. Asked my MP about applying for a TRV and a couple of lawyers they all told me from Yemen it's impossible for her to get an approval.
It's crazy the amount of pictures they have from the first day of our marriage to the last day before I came back to Canada to even deny our marriage I quote from the GCMS notes I received from IRCC written by the officer "
NOTES: 3
Created Date: 2023/11/13
Updated Date: 2023/11/13
Restricted: N
Label: Eligibility
Office: London
Text: Reviewed - appears this may have been a proxy marriage but it is not clear.
Satisfied this is a genuine relationship, they cohabited for a number of years post wedding, have a child
together, have recently travelled to meet in Jordan, seen photos of them at various times and they appear
happy and in a genuine relationship. Seen evidence of communication.
Will PFL on proxy marriage, give them an opportunity to explain whether this was proxy or not. ill explain
if it is a proxy marriage, and excluded I could consider them at CLPs (as state they cohabited for 4 years) if
they consent and provide evidence of cohabitation. "