STEM OPT Application Concern: No Formal Offer Letter, Only Email Confirmation

Hi everyone,
I am currently interning at a company (say A), but I’ve received a full-time offer elsewhere (say company B) that begins in the second week of September.

For context: I interned at A during Fall 2024, and that internship ended in December 2024. Afterward, my manager offered me another internship under OPT from May 2025 to December 2025, which I accepted. However, for this 2025 internship term, she did not issue a new official offer letter, explaining that HR wouldn’t generate another one since I was technically still in their system from my previous internship. Instead, she provided the offer details by email, which includes the start and end dates (december being the end date), working hours, and a one-line description of the role.

Now that I am leaving for the full-time job, I’ll be cutting this internship short. Looking ahead, I’ll be applying for STEM OPT next year, so I will have payslips to show, but no formal offer letter, only that email confirmation. Will that be sufficient? Or is it better to ask the company A to issue an offer letter somehow.

Has anyone else dealt with a similar situation?