Allofs was due a day at the office anyway tomorrow [Sunday] with Bremen hosting Dusseldorf, but his transfer between the two northern Germany clubs means his work will start two hours later than originally planned.
It could not start a minute sooner for Kostner, though, who will be glad to tap into his experience tomorrow [Sunday].
"I think his 13-year spell at Bremen speaks for itself," he said. "The way in which he ensured solidarity and peace and quiet at that club, together with Thomas Schaaf, is impressive.
"His experience and his serious, relaxed and expert attitude mean he fits in perfectly at Wolfsburg.
"He can only really help all of us here."
Given the Wolves' league position, they will take all the help they can get.
They currently find themselves inside the bottom three, yet victory tomorrow [Sunday] could take them level on points with Allofs' former club and into a healthier league position, above their hosts.
"We want to put a run together," said Kostner. "We have won three of our last four games, but the way we lost to Nurnberg in between hurt us."
Hoffenheim are also keen on putting together a streak of results which could take them up the table towards their goal of a place in Europe next season.
"We need more consistency and to go to the limit," said their coach Markus Babbel.
"If we do that, then we can pick up a point or two between now and the winter break."