A formal letter of recommendation from a third party should should not, repeat, not be attempted at this point for the following reasons:
1) All schools, except for a few, are under agreement with AMCAS to only accept LORs thru their formal letter service. A school accepting a letter via another mechanism would be violating that agreement. This is done partly to reduce any fraudulent letters sent on applicants behalf, which was an issue some 20+ years ago
2) Any school receiving a third party letter directly is suppose to reject it, and technically, report it but the latter rarely happens
3) Any school receiving a third party letter as part of a student's own update is much more likely to be questioned, rejected or even investigated as this is considered to open to fraudulent letters
4) The deadline for submitting application materials has passed at a large fraction of schools.
5) If you do submit a letter via AMCAS and a school is willing to accept it, you are by this action implying that you want this to be considered for your application. At schools that are strict about their process may then move your file from review back to evaluation to have this done. You then would be returned to review queue at bottom of pile.
Applicants should only send an update and not a formal LOR. In your update, you can note any new activities and possibly include contact info for the school to verify. My experience has been that most applicants have little to update but more importantly, do not write such a letter in a coherent, concise and professional manner. They also mix updates with interest or intent and do not do it well. All these letters tend to sound much more desperate then the writer intends and many think many students do not have these letters reviewed by anyone before they send them. Additionally, these letters should be relatively short and not go on for more than a few paragraphs. Some I see go on for a few pages without adding to the value of the letter. My rule of thumb for update in either 1 "big" event (eg published) or 3 "small" ones (eg good grades, started new position, added hours to an EC). See below for my standard letter type summary:
You have 5 types of overlapping letters to that can be sent to a medical admission committee
Updates: new info you want to make the committee aware of. The information should be worthwhile and significant. Some schools encourage these buy many schools discourage or list policies not accepting updates.
Thank you: after interview
Letter of Interest: Typically, a post-interview but pre-decision letter that can reiterate and reinforce the school would be a good fit, usually with information you learned from your interview. This usually does not include a promise to attend if selected.
Letter of Intent: Typically written by applicants who have been accepted by one school but are on WL at another preferred school, outlining the reasons why you prefer it. There is little to scant evidence that these are particularly effective. It should be noted these are thought to have even less impact for those who are just on WL with no acceptance.
I will add one other type that is rarely used any more, the Reconsideration Letter: This is an applicant rejected pre-interview who has a large anomaly in their academic background that can be viewed through mitigating circumstances and asks to be reconsidered. With the non-screened/minimally pre-screened secondaries, there are plenty of opportunities for an applicant to express these circumstances.
