Jim Gallagher was due to celebrate his 21st birthday when he was shot on a bus at Fort George on the Strand Road.
He had been released from prison just six days before after serving time for planting a bomb and IRA membership.
A soldier has served a prison sentence for Mr Gallagher's manslaughter.
Fiona Gallagher has said that she would like to know what the solider has to say.
Fiona was the key speaker at the latest in a series of events hosted by the Towards Understanding and Healing Team, which was held on Wednesday.
"Jim got out on Tuesday 11th May and by Monday he was dead. Jim was hit on the base of the neck at the right hand side.
"There were two shots fired and he was hit by one of them and the other went through the left side of the bus," she said.
"When he came out it was his upcoming 21st birthday. Effectively the food and drink that was bought for his birthday ended up being served at his wake."
"I think I would be able to stand eye to eye and say I know you took my brother's life but I want to know what his feelings are."
The sister of an IRA man has said that she would like to meet the soldier who killed her brother in Londonderry in 1976.