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Just lag series A and see if they match
lag the series and calculate correlation coefficient?
Would start by reading through some of the answers here https://stats.stackexchange.com/questions/7975/what-to-make-of-explanatories-in-time-series
Show a plot of lag vs correlation/ do a regression of lagged A and B. Sth easy to understand.
Lag series A and check the correlation?
Look up Granger causality lag selection - there are automated tests for finding the correct test. Look at +/- x lags to see if the causality if one way or two way
Coach
Second granger causality.
I’m not super familiar with vector autoregression but that might be something to look at as well.