Company valuations can take off very quickly: Apple was valued at around $100 billion in mid 2007, and so it has taken the company roughly 11 years to grow its market capitalisation by a factor of ten. However, one year before it first hit $1 trillion, it was worth ~$0.8 trillion (which would have resolved a similar question negative).

Amazon's rise was even more impressive. Amazon has grown from $100 bn to $1 trillion in just over 6 years. And one year before it hit $1 trillion, it was worth ~0.46 trillion (which would have resolved a similar question positive).

Will the first publicly traded company to have a $2 trillion market cap be worth double what it was worth 1 year before reaching $2 trillion?

This resolves when a company whose shares can be bought and sold on a stock exchange achieves a market capitalisation of $2 trillion (adjusted to 2018 prices), AND it was worth less than or equal to $1 trillion one year before (also in 2018 prices). The question will refer to Yahoo Finance's data, or any other reputable financial data service.

Methodology clarification (03/03/19): Current quarter's prices are to be adjusted to mean 2018 prices using FRED's GDP implicit price deflator. If the company is not traded in the US, prices given in the currency in which the stocks are traded are to be converted using the arithmetic mean of FRED's real broad effective exchange rate of the current quarter.