Can I quit the probate process??

As administrator, you are responsible for dealing with the estate assets. Also, unless your mother just bought the house a year or two ago, you would likely be leaving a lot of money on the table if you let the home go to foreclosure. You or your attorney should contact the mortgage holder, and explain that your mother died. Explain that you plan to sell the home as soon as you're able to evict the inhabitant. Hopefully that would stall off foreclosure. After all, the bank would have the same problem with the occupant. Connect with an attorney who handles evictions. It may be that it's possible to begin the eviction process by giving either a 30-day or 60-day notice (whichever is appropriate) to at least start things. In reality, in most of these situations people buy out the occupant by giving them enough money for first and last month's rent and security deposit at a new place. That agreement would need to be drafted by your attorney, with careful timing on paying the money (e.g., perhaps paying $ directly to a new landlord, rather than to the old boyfriend) so he doesn't take the money and stay there. I've heard of people paying as much as $5,000-$10,000 to get people out.

Please note that under federal law a mortgage lender cannot foreclose for six months after an administrator is appointed.  Within the six month period, you should not be lending funds to the estate to pay for the mortgage.  If you cannot sell the property within the six month period and the lender does not exercise forebearance in light of covid (which is provided for by the CARES Act), the house will go into foreclosure.