Saudi Arabia has embarked on a global charm offensive.

In the last few days it has appointed its first-ever female ambassador to its top diplomatic post - Washington DC - while its de facto leader, the controversial Crown Prince Mohammed bin Salman, has just concluded a high-profile tour of Asia, discussing billions of dollars' worth of trade and investment deals in China, Pakistan and India.

Less than five months have elapsed since the West recoiled in horror over the grisly, planned murder of Saudi journalist and critic Jamal Khashoggi inside Saudi Arabia's consulate in Istanbul.

The CIA and most western intelligence agencies concluded that the crown prince, known by his initials MBS, was most likely behind the murder, something Saudi officials strongly deny.

Previously feted in Western cities, MBS was largely shunned by the West at the recent G20 summit in Buenos Aires.

He faces ongoing condemnation in the Western media, not just for the Khashoggi affair, but for locking up peaceful protesters, including women, and for pursuing a catastrophic war in Yemen.

So what does he do? He turns eastwards, just as other Gulf Arab leaders did in 2011 following European criticism of autocratic practices in their region. He got a red-carpet welcome.

In Pakistan, a nuclear-armed country now in dire financial difficulties, MBS dispensed Saudi largesse and was honoured with a 21-gun salute, an escort of fighter jets, and a gift of a gold-plated submachine gun.

In India he was warmly greeted by Prime Minister Narendra Modi and went on to discuss huge investment deals, primarily in the energy sector. And in China, Asia's emerging superpower, the crown prince held talks with President Xi Jinping and signed a $10bn (£7.6bn) refinery deal.

Saudi royals do not travel alone. If you are the crown prince and de facto ruler, you take with you a vast entourage of 1,100 in several planes, occupying hundreds of hotel rooms, as well as a personal, portable gym.

The entourage includes journalists from the state-controlled media who can then report back to the population how well their leader is being received.

MBS's position inside Saudi Arabia was already considered secure even before this trip - there are no other serious contenders for the throne. But being warmly embraced in important Asian countries plays well to a Saudi audience and helps dispel the notion of him being a pariah in the wake of the Khashoggi murder.

America though, will be a tougher nut to crack. It is no coincidence that the newly appointed Saudi ambassador to Washington is a woman.

Princess Reema bint Bandar Al Saud is a successful businesswoman in her own right. She has also championed a greater role for Saudi women in society.

But she will have to contend with a highly critical Congress, and US media that have reported extensively on the shortcomings in Saudi Arabia's human rights record.

Her predecessor in the post, Prince Khalid bin Salman Al Saud, departed Washington in a hurry after the Khashoggi affair. He has been accused of complicity in the journalist's murder, which he denies, and was told not to return without a clear explanation of what happened.

So where does all this leave Europe? In short, in a quandary.

Saudi Arabia is Britain's biggest Middle East trading partner with up to 50,000 British jobs dependant on it.

With its enormous oil wealth, the desert kingdom is a massive market for exporters and - controversially - a major buyer of British weaponry, something the opposition leader Jeremy Corbyn has promised to end.

Relations with Britain and France are cooler, but neither has taken significant measures against Riyadh. Germany, however, has reacted to the Khashoggi killing with a freeze on arms exports, something that now threatens to disrupt the UK-Saudi defence relationship since parts of the Typhoon fighter jet are produced in Germany.

Saudi Arabia's message to the West appears to be twofold. By drawing closer to big, important nations in Asia, it says: "We do have other friends around the world and they're happy to do business with us." By sending a young female ambassador to Washington, it says: "We know we have ground to make up so we are happy to listen to what you have to say."

What matters to Saudi Arabia's critics though, is whether any of this will make any difference to the way in which all political dissent has been suppressed at home, something that continues to embarrass those Western governments doing business with Riyadh.