I'd keep trying to get through on the phone to confirm they received it. How long ago did you write, and did you send it recorded / keep proof of postage?
Which benefit was it for? Idk about UC but for ESA/PIP you can request a mandatory reconsideration (the first stage of appeal) either by phone or letter, no need to fill in a form. Personally I phone just to get the request in within the time limit, and tell them I will follow up with a letter setting out my reasons for requesting MR rather than discuss via phone. If you've asked for a copy of the decision/hcp's report they should give you more time to get the MR request in once you've received that.
Afaik there's no limit to how long they can take to carry out a mandatory reconsideration
E2a did your partner give permission for you to communicate with DWP on their behalf, either in/enclosed with your letter or previously that they would have on record?