Teddy made his debut on Saturday against Peterborough, and Peter says:
"Teddy's fitness levels are excellent, and he is up there with the best of them with his training, so it not a problem whatsoever.
"It is just that game sharpness that he needs but everybody needs that, no matter how hard you work physically.
"Saturday was the first time the players had played with him; you could see that he is intelligent and we have to get the players to buy into that, because you could see him make certain movements that were first class but we didn't have the quality to pick him out at certain times.
"But I am sure he will be a major asset to us, not just in the playing sense, but obviously in helping players in that forward area and getting players to think about the game on the pitch.
"People always say he hasn't got pace, but the thing is, he is always five yards quicker upstairs than everybody else.
"I have watched him in training close up now, having seen him from afar before, and he has got great game awareness and football intelligence - which is something we need to add to our game.
"He drags people out of position and makes unselfish movement to create space for others and that is what we are looking to rub off on to the team."
West Ham are without Steve Lomas and Bobby Zamora at Colchester, and Peter says:
"The two of them have been excellent in their training and we were happy as Larry coming back from Sweden with everyone fit - but on the first day back, unfortunately Steve had the accident with his ankle.
"We don't want him to be out too long out as I am sure he will be a major influence, and Bobby has also been working hard as well, so hopefully both of them will be fighting fit come the seventh."
Peter is looking for an improvement on the Peterborough performance, and he says:
"We had a hard nine or 10 days in Sweden and I think in the second half at Peterborough that showed.
"We started quite brightly for the first 30 minutes, but just before half time when we conceded the goal we stopped passing and doing the things that we had been doing earlier in the game.
"Okay, there was the length of the grass but I thought the movement became a bit stagnant and maybe because that was because they had been doing two or three sessions a day in Sweden, had done the travelling, and had tired legs.
"But we are looking for better than we got in the second half, obviously.
"It is probably the only time in the year that you train as hard the morning of games so players' bodies are not used to playing and training hard on the same day.
"It is a big time fitness-wise and you hope you are getting sharper every game, but the main aim is to make sure everyone is fully fit and raring to go come August 7th, which is a vital game for us.
"We are looking for more progression towards that."