Jean, from Birkenhead, launched FFFJ after exsoldier Stephen Wynne killed her daughter, Chantel, 27, with a meat cleaver before disposing of her remains.
Jean said the next stage for FFFJ was to acquire a house available for victims' relatives to visit and stay at.
However, the FFFJ
had promised to look for a new lawyer, she added.
Actress Crissy Rock, a patron of FFFJ
, was among those supporting the Jones family as was Mayor of Liverpool Joe Anderson.
The pair struck up a conversation and Crissy expressed an interest in FFFJ, telling her new friend she would help out if she could.
The centre, which FFFJ is able to run thanks to funding from local businessman and Wolverhampton Wanderers owner Steve Morgan, is open every week day.
Joseph", 14, started up the children's branch of FFFJ when his mum was killed.
FFFJ hopes the move, funded by the Morgan Foundation, will give children access to the services and help they need, with staff who are trained to deal with their situations.
Mr Jones said: "Doing things with FFFJ makes us feel better and helped us come to terms with what has happened.
Jean Taylor, founder of FFFJ, whose sister, son and daughter were all killed through crime said she would continue to support the Jones family in their quest for justice.
FFFJ opened a new drop-in centre in Liverpool's Seymour Street in July last year, offering advice and support to victims families.
The FFFJ centre is open from 10am to 4pm Monday to Friday, at 19 Seymour Terrace, Liverpool.