I graduated last year and my advisor passed away unexpectedly soon after. What should I do now for subsequent academic job searches?

I received a PhD in mathematics last May. Last December, my advisor passed away quite unexpectedly.

My advisor was an extraordinary person; in addition to being a fantastic advisor mathematically, he was a wonderful mentor who I always thought of as a friend - this is very much a personal loss for me. My initial emotional response was that I should clearly leave mathematics forever. Rationally, that seems uncalled for. Before all of this, I had been aiming for academic jobs in mathematics. However, I expect that a recommendation (as well as other help) from one's advisor is a significant part of an academic job application (for example, this recent answer states that the letter from one's advisor is read first even when applying for a tenure-track job after a postdoc).

How does one go about an academic job search when one's advisor has passed away?

For example, my advisor wrote a letter for me for my job search out of grad school. Does one try to use that letter (via perhaps my graduate department) for subsequent job applications? Do I mention in every cover letter from now on end that my advisor has died (that seems horrifying, since I like my vague sense of denial)?

I am in the first year of a (3-yr) postdoc, so I won't be on the job market for a while (in fact, it seems simultaneously very soon and too far away). Of course I can tell that my productivity and motivation have slumped in the last few months, and I know that I should try to get back into gear as soon as possible.

---

Related questions:

While in more of a 'denial' stage, I asked this question to try to get at this.

The analogous question for current graduate students was asked here and here.

There are several questions about dealing with not having a letter from one's PhD advisor on ac.se, such as this one, or this one, or this one.