Beckingham, pictured, guided the Wasps to third from bottom last season before the club received a reprieve from relegation in the Football Association's annual reshuffle of the Non-League pyramid after succeeding Simon Funnell at East Court last November.
He resigned on Monday to work alongside Clive Cook as the successors to Tim Dixon at Reachfields following his weekend departure from the Cannons, currently sitting one place above the third from bottom Wasps in the table.
In a statement confirming Beckingham's departure, Tramontin wished their former manager well and thanked skipper Jon Difford for agreeing to hold the fort until a new manager is appointed.
Tramontin said: “Tony has decided to take up an offer from Hythe. We are all disappointed with his decision but we wish him all the best and thank him for his efforts at East Grinstead during his two spells in charge.
“I’m delighted that Jon has agreed to take on managerial responsibilities whilst carrying on playing and allowing us the time to ensure we appoint the right candidate to take the club forward."
He added: “Anyone with suitable experience who would be interested in the post can email me."
Unless an early appointment is made, Difford will take charge for the first time next Tuesday night when the Sparks go in search of a first league home win of the campaign when they host Hastings United.
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