Jasso made the appointment during Monday’s Deming City Council meeting, and it was approved by a unanimous vote of the council.
Rincon’s appointment becomes effective Thursday, February 12th.
Rincon said she has been a Deming resident for over 25 years, loves the community and wants to serve to help Deming continue to prosper and improve for future generations.
She will serve until the municipal election in March of 2016, and will be eligible to run for a four-year term in that election.
Rincon was one of four people who expressed interest in being appointed to fill the remainder of Franklin’s term.
Monday night’s meeting was the last for Franklin, who is moving to Lubbock to be near family and major medical resources.
Franklin was first elected to the Deming City Council in 2002 to fill a two-year term, and has been reelected to four-year terms every voting cycle since.
At the meeting, Franklin was presented with an appreciation plaque, a bouquet of flowers and a key to the city.