The highly rated 20-year-old, who spent last season on loan at Cheltenham Town, has played 25 times this season after arriving at Sincil Bank on loan in the summer.
Griffiths, who has been capped twice at England Under 18 level, penned a new four year contract with the Baggies in the summer - and now he looks set to remain at Lincoln until the end of the season after former Albion man Appleton confirmed the recall deadline on his loan deal has passed.
Appleton told Lincolnshire Live: “We’ve not heard from them and the deadline has passed so he will be with us for the rest of the season.
“He’s got stronger and stronger. He had a very difficult start as we all know in the first five or six games, but since then his performances have grown and he’s improved with his feet as well.
“That’s been recognised, not only by myself but by the people at West Brom as well.
“We knew his capabilities as a goalkeeper – his handling, his shot-stopping skills – but I think we’ve helped him develop as a player, which is part and parcel of the job as well.”