After you upgrade the Trader's Tent to level 2, click on the Jeweler's Stall and the quest "Total Recall" will appear. 
 
The quest includes 10 stages with a time limit.
 
Stage 1 (24 hours)
Collect 22 shovels (in friends’ cities) 
Collect 7 flasks (Beach House, Summer Mansion) 
Collect 32 backpacks (Summer House, Upgraded Summer House) 
 
Stage 2 (24 hours)
Collect 8 scotch tapes (Auto Repair Shop) 
Collect 40 stepladders (Convenience Store, Upgraded Convenience Store) 
Collect 36 night visions (Subway Station, Upgraded Subway Station, Central Station, Eastern Station) 
 
Stage 3 (24 hours)
Collect 9 tool kits (Shopping Center) 
Ask friends for 15 repair kits 
Collect 19 saws (Colonial House, Upgraded Colonial House) 
 
Stage 4 (24 hours)
Collect 42 pencils (Stationery Shop, Upgraded Stationery Shop) 
Collect 2 files with documents (City Hall) 
Train 6 architects (University) 
 
Stage 5 (24 hours)
Collect 16 sweets (Candy Factory, Upgraded Candy Factory when collecting cherry cupcake, toffee apple, cherry pie, choco-log, cake with berries, chocolate, eclair, honey pie, cheesecake)
Ask friends for 14 sunglasses 
Collect 12 strawberry cocktails (Pub, Upgraded Pub) 
 
Stage 6 (24 hours)
Collect 9 light bulbs (Electronics Plant, Upgraded Electronics Plant when collecting mouse) 
Ask friends for 14 neon lamps 
Produce 14 lots of cables (Construction Factory, Upgraded Construction Factory, Construction Megafactory) 
 
Stage 7 (24 hours)
Collect 17 nails (in friends’ cities) 
Collect 15 planks (Cargo Port)
Train 6 builders (College)
 
Stage 8 (24 hours)
Collect 8 leather sofas (Furniture Factory) 
Collect 32 hanging baskets (Recreational Cottage, Upgraded Recreational Cottage) 
Collect 16 chairs (Family Restaurant)
 
Stage 9 (24 hours)
Collect 2 office chairs (Sky Tree) 
Collect 45 tubes of glue (Shoe Shop, Upgraded Shoe Shop) 
Collect 9 scribe compasses (Country Cottage, Wooden House)  
 
Stage 10 (24 hours)
Collect 7 magic lanterns (Cinema) 
Ask friends for 13 amulets 
Collect 12 lucky coins (Guardian of the Valley) 

 After restoring the Jeweler's Stall, you can produce cut gems there: