Ship A (with TS) TL's Ship C
Ship B use primary attack on Ship C

Can Ship B use TL of Ship A for modify its attack dice?

Yes. Basically, unless the effect you're looking at cares whether you have the enemy ship "locked" (e.g. Omega Leader, the OS-1 Arsenal Loadout title for gunboats), you can use the Target Lock of the ship with Targeting Synchronizer normally.

The relevant question in the FAQ doesn't mention TS specifically, but it'ss about what counts as a game effect that instructs you to spend a Target Lock, which is TS's wording. The answer isn't super well worded--it kinda reads like they were answering a different question--but it's the best guidance we have right now.

FAQ 4.4.1 p 23:

Q: What are examples of game effects that instruct a player to spend a target lock?
A: The cost for a secondary weapon such as Proton Torpedoes, using pilot abilities like Lieutenant Colzet, or spending a target lock during the "Modify Attack Dice" step to reroll attack dice are all examples of spending a target lock.
Removing a target lock or assigning a blue target lock token to another ship are not examples of spending a target lock.