Ficus are sensitive when moved to a new location, and they often show their unhappiness by shedding leaves. As long as there isn't a draft in the new spot, they'll settle down and releaf.
The stickiness you describe, however, is bad news; it sounds like honeydew -- the waste of sap-eating insects like spider mites, scale, or mealy bugs. Scale and mealy bugs are visible on the plant. Scale look like little gray or brown bumps. Mealy bugs look like little white cottony masses. Spider mites are so tiny that you can't usually see them, but you might see webs or feel a gritty feeling between your fingers if you wipe them along leaves and branches. If it's scale or mealy bugs, buy a houseplant insecticide at the garden center, and apply it according to the label.
You can also dab the insects individually with a Q-tip dipped in rubbing alcohol, but I've found that to be overwhelming on large plants. If it's spider mites, take the ficus back outside and wash it thoroughly (tops and bottoms of the leaves, all branchs and the trunk) with a strong blast from the garden hose. Spider mites are so tiny and vulnerable that a harsh blast of water will kill more than 90 percent of them.