Sorry I might be picking this up wrong - you think he has indicated that I would be unemployable (in his personal opinion) by education department due to my interactions with the school when advocating for my child?
In real life short answer is: yes because thats why he chose to use that wording and it was not the education department it was your current job.
Long answer
On rereading your posts
You said
"apparently this is not the first time your staff member has had complaints made about her social media usage" & then goes onto say I would be "unemployable in the future by education services".
Plus
within his complaint he has made alot of false allegations
I think you need to read the letter carefully.
If it is one paragraph eg
apparently this is not the first time your staff member has had complaints made about her social media usage and because of this large digital footprint will be unemployable in the future by education services....
This is fluff and huffing because your post passes or fails your employers SM standards not his employers. In his mind you should be sacked when his standards were applied.
Or is it in summary of all the other points
apparently this is not the first time your staff member has had complaints made about her social media usage
and
apparently your staff member was seen eating icecream and caused the last snow fall
and
As a result of these numerous miscounduct she will be unemployable in the future by education services
Thats different and speaks to the whole relationship. But you are still sacked
Your legal will advise if that type of letter is actionable or not.
In general
You wrote one SM post which would not have gotten him sacked.
He located your employer then wrote a letter which worst case could have gotten you sacked.
What motivated him to go from thinking/saying what an "knobber" that random parent must be to I am going to get that parent sacked from their job.
If he only wrote to your employer and not contacted your friend's employer (if she has one) when she started the discussion, why is that?
If as you say you have no out of school community conection with him the direct link is your ongoing interactions with the school.
In real life with no social connection his first impressions will come from an in-person introduced to you as parent of child X or via the other professionals (not just teachers) in contact with your son.
Sorry but any Head will be dealing with all types of people and it take a lot of (subjectively) negitive interactions to go from she is a "sweet dear person" to "knobber" to "sack her" and one (mildly) nasty SM post is a very low tipping point.
And that is a real life problem for how your sons ongoing education is managed.
Anyway
Their is a social connection you are not aware of being one or more people in the FB group.
And if you dont do a lot of SM the person will likely have friend level access to all your other content.
So wording
apparently
I am reading this as his stating that he has been informed by someone
a) but is unable to submit proof that one or more named individual showed him SM and the letter to your employer ( well they claimed to have sent it, you would have been informed so the sent bit did not happen)
b) employed/connected to your job
c) who is a random gossip who heard it in the post office
this is not the first time
so someone a) or b) is making up stories of being aware of a prior investigation
your staff member has had complaints made
he is making a statement without proof on what happened more that one time in your employers internal complaints process (wording more likely person b because format construction is not a sending in their letter )
about her social media usage
In real life the Head trusts whoever is making up the story of the prior complaint. If they also are your SM friend they set out to cause a break in the relationship between you and the Head.
Rambling done.