Jayne Hickey and her son Christian were shot when two men knocked on their front door in Gillingham Road in Eccles, Salford on 12 October.
The gun was one of two firearms seized when a vehicle was stopped in Faulkner's Lane, Mobberley in Cheshire on 15 December at about 21:20 GMT.
Two men have appeared in court charged with possession of firearms.
A weapon has also been linked to a man's shooting in Ashton-in Makerfield, Wigan on 30 March.

The striker's only goal this season, having been transferred from Derby County, came in the 5-1 win over Malta.
"Of course, for a striker, I think it is always a bit of a concern, but I don't really think too much about that," he said of his goal drought.
"This can probably be a little bit of a release for me."
Martin has played six times for his English Championship club since scoring one and also winning a penalty in Attard.
"Coming away on international duty away from the pressures of club level and try to perform here, it is a different set-up, a different vibe and a different feeling," said the 27-year-old.
"So hopefully I can use this as a bit of a catalyst for me and I can continue that and take it back to club level."
Scotland coach Gordon Strachan surprised many observers - including the player himself - by handing a starting place to Martin as he earned his ninth cap against Malta.
"I think I was perhaps a bit fortunate to start the last game," the striker said ahead of Saturday's home qualifier against Lithuania. "I wasn't expecting it really.
"I think there were others in line for it who were just as deserving.
"Leigh Griffiths was unfortunate with the injury he had, especially with the start of the season he had and how he played last season."
Martin is hopeful that his style of play will again be what Strachan is looking for against Lithuania.
"I felt like I did okay and I managed to score and won the penalty for us somehow," he said.
"I've had a few opportunities now - done okay in some and not so well in others - but I think there's more to come from myself.
"It is about consistency of performance and, if I keep getting picked, hopefully that will come.
"We'll have to see how the manager thinks, but hopefully I've done enough."
Martin admits that the Scots will be favourites to beat Lithuania but warns that the visitors will prove tricky opponents.
"Perhaps the public think that Lithuania aren't going to be too good and we know different to that," he said.
"I think they are going to be an extremely tough team, but I think, after such a convincing result in the first game away from home, a full crowd will be expectant of a win on Saturday."
A gun that is believed to have been used to shoot a mother and her seven-year-old son has been seized by police.
[NEXT_CONCEPT]
Chris Martin hopes that his goal in Scotland's last World Cup qualifier will be enough to retain his place despite a barren spell with Fulham.