Annes, where the Australian bogeyed his last four holes and finished one shot behind in the British Open.
He died at a hospice near his home in Lytham St Annes on Sunday night, following a short illness.
But Williams, originally from Lytham St Annes, is keen to stress that reports of an imminent takeover are incorrect.
The firm announced it is to apply to resume fracking at its Anna's Road site in St Annes on Monday.
Annes, when he drove into a car park and then chipped onto the green before sinking a 30-footer for birdie.
Scout leader and school governor Thomas Westall from Lytham St Annes becomes a MBE for services to children and young people.
Her three-stroke triumph at Royal Lytham and St Annes in August made her the first Scottish woman to clinch victory in a major.
Cuadrilla has applied to Lancashire County Council to frack for shale gas at its Anna's Road site in St Annes and Banks, near Southport.
BBC: Lancashire election candidates asked to oppose fracking
The firm has applied to Lancashire County Council to frack for shale gas at its Anna's Road site in St Annes and Banks, near Southport.
BBC: Lancashire's shale gas estimated at ?136bn by Cuadrilla
Four-time major winner Mickelson got a late invitation to compete in the European Tour event to complete final preparations for Royal Lytham and St Annes next week.
Annes in 2012 was the closest he had got to winning one of the sport's four blue riband events, letting the Claret Jug slip from his grasp and into Ernie Els' hands.
Elaine Bertenshaw from Lytham St Annes who is a volunteer for Lancashire Constabulary was also appointed MBE for services to policing and the community as was Burnley's Emma Hamlen, a volunteer for the youth offending team, for services to young people in Lancashire and Jacqueline McGrew, chair of Whitebirk Residents' Association in Blackburn, for services to the community.
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