On 30 June 2018 a one-month penalty-free grace period was eventually published on the Hungarian government’s website, for the time being only in Hungarian.
Unofficial summary in English:
As of July 1, businesses are required to sent each and every invoice on which the VAT is at least HUF 100,000 to the Hungarian tax authorities. As this is a major operation for many taxpayers, the Hungarian government has now announced that taxpayers that are affected by this change and who act as partners in this transition period are not penalized if the invoicing system they are using is not yet able to provide live invoice data.
The Finance Minister said that for a smooth transition, he asked the that if the invoice data were received by 31 July by the Tax office, it would not impose any sanctions on the taxpayers. It may happen that an enterprise is not ready to provide data by July 1, even though it has started the preparation to do so.
Source: Kormany (in Hungarian)