The most important thing is not to cash more social security checks of your wife. If there are any more direct deposits into the bank account, just let it stay in the bank account. They will be automatically drawn back by the SSA. Don't spend it. Don't take it out.
Usually, the funeral home should have reported the death to the Social Security Administration.
I would prefer personally to walk into a local social security administration office and bring a copy of the death certificate. Document the date, place you went and with whom you talked.
I am so sorry for your loss.
Please feel free to follow up. The citation and website link below are for your further reference on how to report your wife's passing to the SSA.
Fiona Chen, MPA, Ph.D., CPA, ABV, CFF, CITP
"You should give the funeral home the deceased person's Social Security number if you want them to make the report. If you need to report a death or apply for benefits, call 1-***-***-**** ( TTY 1-***-***-****). You can speak to a Social Security representative between 7 AM and 7 PM Monday through Friday."