Shopify does not permit adding products having duplicate variants. For example, consider the following product having Variant 1 and Variant 3 as duplicates.

Parent ProductFull sleeve t-shirt
Variant 1Red, Small
Variant 2Red, Medium
Variant 3
Red, Small
Variant 4Red, Large

Such products when pulled from Amazon seller account cannot be pushed to Shopify. Either Variant 1 or Variant 3 (from the example) can be pushed. The Duplicate Variant Preference settings (on the Push Settings page) can be used to guide the Connectr app in determining which of the two duplicate variants to push into Shopify. 

On selecting 'Merchant Fulfilledthe duplicate variant having fulfillment type as Merchant will be pushed to Shopify leaving out the other duplicate variant. Whereas selecting 'Amazon Fulfilled' gives the variant having fulfillment type as Amazon the preference.